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17 changes: 9 additions & 8 deletions Mathlib/Analysis/Normed/Group/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -608,11 +608,12 @@ end NNNorm
section ENorm

@[to_additive (attr := simp) enorm_zero]
lemma enorm_one' {E : Type*} [TopologicalSpace E] [ESeminormedMonoid E] : ‖(1 : E)‖ₑ = 0 := by
lemma enorm_one' {E : Type*} [TopologicalSpace E] [Monoid E] [ESeminormedMonoid E] :
‖(1 : E)‖ₑ = 0 := by
rw [ESeminormedMonoid.enorm_zero]

@[to_additive exists_enorm_lt]
lemma exists_enorm_lt' (E : Type*) [TopologicalSpace E] [ESeminormedMonoid E]
lemma exists_enorm_lt' (E : Type*) [TopologicalSpace E] [Monoid E] [ESeminormedMonoid E]
[hbot : NeBot (𝓝[≠] (1 : E))] {c : ℝ≥0∞} (hc : c ≠ 0) : ∃ x ≠ (1 : E), ‖x‖ₑ < c :=
frequently_iff_neBot.mpr hbot |>.and_eventually
(ContinuousENorm.continuous_enorm.tendsto' 1 0 (by simp) |>.eventually_lt_const hc.bot_lt)
Expand Down Expand Up @@ -650,7 +651,7 @@ end ENorm

section ESeminormedMonoid

variable {E : Type*} [TopologicalSpace E] [ESeminormedMonoid E]
variable {E : Type*} [TopologicalSpace E] [Monoid E] [ESeminormedMonoid E]

@[to_additive enorm_add_le]
lemma enorm_mul_le' (a b : E) : ‖a * b‖ₑ ≤ ‖a‖ₑ + ‖b‖ₑ := ESeminormedMonoid.enorm_mul_le a b
Expand All @@ -672,7 +673,7 @@ end ESeminormedMonoid

section ENormedMonoid

variable {E : Type*} [TopologicalSpace E] [ENormedMonoid E]
variable {E : Type*} [TopologicalSpace E] [Monoid E] [ENormedMonoid E]

@[to_additive (attr := simp) enorm_eq_zero]
lemma enorm_eq_zero' {a : E} : ‖a‖ₑ = 0 ↔ a = 1 := by
Expand Down Expand Up @@ -752,7 +753,7 @@ end Induced
section SeminormedCommGroup

variable [SeminormedCommGroup E] [SeminormedCommGroup F] {a b : E} {r : ℝ}
variable {ε : Type*} [TopologicalSpace ε] [ESeminormedCommMonoid ε]
variable {ε : Type*} [TopologicalSpace ε] [CommMonoid ε] [ESeminormedMonoid ε]

@[to_additive]
theorem dist_eq_norm_div (a b : E) : dist a b = ‖a / b‖ := by
Expand Down Expand Up @@ -804,7 +805,7 @@ theorem norm_multiset_sum_le {E} [SeminormedAddCommGroup E] (m : Multiset E) :
‖m.sum‖ ≤ (m.map fun x => ‖x‖).sum :=
m.le_sum_of_subadditive norm norm_zero.le norm_add_le

variable {ε : Type*} [TopologicalSpace ε] [ESeminormedAddCommMonoid ε] in
variable {ε : Type*} [TopologicalSpace ε] [AddCommMonoid ε] [ESeminormedAddMonoid ε] in
theorem enorm_multisetSum_le (m : Multiset ε) :
‖m.sum‖ₑ ≤ (m.map fun x => ‖x‖ₑ).sum :=
m.le_sum_of_subadditive enorm enorm_zero.le enorm_add_le
Expand All @@ -813,13 +814,13 @@ theorem enorm_multisetSum_le (m : Multiset ε) :
theorem norm_multiset_prod_le (m : Multiset E) : ‖m.prod‖ ≤ (m.map fun x => ‖x‖).sum :=
m.apply_prod_le_sum_map _ norm_one'.le norm_mul_le'

variable {ε : Type*} [TopologicalSpace ε] [ESeminormedCommMonoid ε] in
variable {ε : Type*} [TopologicalSpace ε] [CommMonoid ε] [ESeminormedMonoid ε] in
@[to_additive existing]
theorem enorm_multisetProd_le (m : Multiset ε) :
‖m.prod‖ₑ ≤ (m.map fun x => ‖x‖ₑ).sum :=
m.apply_prod_le_sum_map _ enorm_one'.le enorm_mul_le'

variable {ε : Type*} [TopologicalSpace ε] [ESeminormedAddCommMonoid ε] in
variable {ε : Type*} [TopologicalSpace ε] [AddCommMonoid ε] [ESeminormedAddMonoid ε] in
@[bound]
theorem enorm_sum_le (s : Finset ι) (f : ι → ε) :
‖∑ i ∈ s, f i‖ₑ ≤ ∑ i ∈ s, ‖f i‖ₑ :=
Expand Down
5 changes: 0 additions & 5 deletions Mathlib/Analysis/Normed/Group/Continuity.lean
Original file line number Diff line number Diff line change
Expand Up @@ -135,11 +135,6 @@ instance NormedGroup.toENormedMonoid {F : Type*} [NormedGroup F] : ENormedMonoid
enorm_eq_zero := by simp [enorm_eq_nnnorm]
enorm_mul_le := by simp [enorm_eq_nnnorm, ← coe_add, nnnorm_mul_le']

@[to_additive]
instance NormedCommGroup.toENormedCommMonoid [NormedCommGroup E] : ENormedCommMonoid E where
__ := NormedGroup.toENormedMonoid
__ := ‹NormedCommGroup E›

end Instances

section SeminormedGroup
Expand Down
50 changes: 25 additions & 25 deletions Mathlib/Analysis/Normed/Group/Defs.lean
Original file line number Diff line number Diff line change
Expand Up @@ -111,36 +111,30 @@ class ContinuousENorm (E : Type*) [TopologicalSpace E] extends ENorm E where
/-- An e-seminormed monoid is an additive monoid endowed with a continuous enorm.
Note that we do not ask for the enorm to be positive definite:
non-trivial elements may have enorm zero. -/
class ESeminormedAddMonoid (E : Type*) [TopologicalSpace E]
extends ContinuousENorm E, AddMonoid E where
class ESeminormedAddMonoid (E : Type*) [TopologicalSpace E] [AddMonoid E]
extends ContinuousENorm E where
enorm_zero : ‖(0 : E)‖ₑ = 0
protected enorm_add_le : ∀ x y : E, ‖x + y‖ₑ ≤ ‖x‖ₑ + ‖y‖ₑ

-- see Note [lower instance priority]
attribute [instance 200] ESeminormedAddMonoid.toAddMonoid

/-- An enormed monoid is an additive monoid endowed with a continuous enorm,
which is positive definite: in other words, this is an `ESeminormedAddMonoid` with a positive
definiteness condition added. -/
class ENormedAddMonoid (E : Type*) [TopologicalSpace E]
class ENormedAddMonoid (E : Type*) [TopologicalSpace E] [AddMonoid E]
extends ESeminormedAddMonoid E where
enorm_eq_zero : ∀ x : E, ‖x‖ₑ = 0 ↔ x = 0

/-- An e-seminormed monoid is a monoid endowed with a continuous enorm.
Note that we only ask for the enorm to be a semi-norm: non-trivial elements may have enorm zero. -/
@[to_additive]
class ESeminormedMonoid (E : Type*) [TopologicalSpace E] extends ContinuousENorm E, Monoid E where
class ESeminormedMonoid (E : Type*) [TopologicalSpace E] [Monoid E] extends ContinuousENorm E where
enorm_zero : ‖(1 : E)‖ₑ = 0
enorm_mul_le : ∀ x y : E, ‖x * y‖ₑ ≤ ‖x‖ₑ + ‖y‖ₑ

-- see Note [lower instance priority]
attribute [instance 200] ESeminormedMonoid.toMonoid

/-- An enormed monoid is a monoid endowed with a continuous enorm,
which is positive definite: in other words, this is an `ESeminormedMonoid` with a positive
definiteness condition added. -/
@[to_additive]
class ENormedMonoid (E : Type*) [TopologicalSpace E] extends ESeminormedMonoid E where
class ENormedMonoid (E : Type*) [TopologicalSpace E] [Monoid E] extends ESeminormedMonoid E where
enorm_eq_zero : ∀ x : E, ‖x‖ₑ = 0 ↔ x = 1

/-- An e-seminormed commutative monoid is an additive commutative monoid endowed with a continuous
Expand All @@ -149,35 +143,41 @@ enorm.
We don't have `ESeminormedAddCommMonoid` extend `EMetricSpace`, since the canonical instance `ℝ≥0∞`
is not an `EMetricSpace`. This is because `ℝ≥0∞` carries the order topology, which is distinct from
the topology coming from `edist`. -/
class ESeminormedAddCommMonoid (E : Type*) [TopologicalSpace E]
extends ESeminormedAddMonoid E, AddCommMonoid E where

-- see Note [lower instance priority]
attribute [instance 200] ESeminormedAddCommMonoid.toAddCommMonoid
@[deprecated "Use `[AddCommMonoid E] [ESeminormedAddMonoid E]` instead." (since := "2026-04-14")]
structure ESeminormedAddCommMonoid (E : Type*) [TopologicalSpace E]
extends AddCommMonoid E, ESeminormedAddMonoid E where

set_option linter.deprecated false in
/-- An enormed commutative monoid is an additive commutative monoid
endowed with a continuous enorm which is positive definite.

We don't have `ENormedAddCommMonoid` extend `EMetricSpace`, since the canonical instance `ℝ≥0∞`
is not an `EMetricSpace`. This is because `ℝ≥0∞` carries the order topology, which is distinct from
the topology coming from `edist`. -/
class ENormedAddCommMonoid (E : Type*) [TopologicalSpace E]
@[deprecated "Use `[AddCommMonoid E] [ENormedAddMonoid E]` instead." (since := "2026-04-14")]
structure ENormedAddCommMonoid (E : Type*) [TopologicalSpace E]
extends ESeminormedAddCommMonoid E, ENormedAddMonoid E where

/-- An e-seminormed commutative monoid is a commutative monoid endowed with a continuous enorm. -/
@[to_additive]
class ESeminormedCommMonoid (E : Type*) [TopologicalSpace E]
extends ESeminormedMonoid E, CommMonoid E where
attribute [nolint docBlame] ENormedAddCommMonoid.toENormedAddMonoid

-- see Note [lower instance priority]
attribute [instance 200] ESeminormedCommMonoid.toCommMonoid
set_option linter.existingAttributeWarning false in
/-- An e-seminormed commutative monoid is a commutative monoid endowed with a continuous enorm. -/
@[to_additive,
deprecated "Use `[CommMonoid E] [ESeminormedMonoid E]` instead." (since := "2026-04-14")]
structure ESeminormedCommMonoid (E : Type*) [TopologicalSpace E]
extends CommMonoid E, ESeminormedMonoid E where

set_option linter.deprecated false in
set_option linter.existingAttributeWarning false in
/-- An enormed commutative monoid is a commutative monoid endowed with a continuous enorm
which is positive definite. -/
@[to_additive]
class ENormedCommMonoid (E : Type*) [TopologicalSpace E]
@[to_additive,
deprecated "Use `[CommMonoid E] [ENormedMonoid E]` instead." (since := "2026-04-14")]
structure ENormedCommMonoid (E : Type*) [TopologicalSpace E]
extends ESeminormedCommMonoid E, ENormedMonoid E where

attribute [nolint docBlame] ENormedCommMonoid.toENormedMonoid

/-- A seminormed group is an additive group endowed with a norm for which `dist x y = ‖-x + y‖`
defines a pseudometric space structure. -/
class SeminormedAddGroup (E : Type*) extends Norm E, AddGroup E, PseudoMetricSpace E where
Expand Down
2 changes: 1 addition & 1 deletion Mathlib/Analysis/Normed/Group/Indicator.lean
Original file line number Diff line number Diff line change
Expand Up @@ -23,7 +23,7 @@ open Set

section ESeminormedAddMonoid

variable {α ε : Type*} [TopologicalSpace ε] [ESeminormedAddMonoid ε]
variable {α ε : Type*} [TopologicalSpace ε] [AddMonoid ε] [ESeminormedAddMonoid ε]
{s t : Set α} (f : α → ε) (a : α)

lemma enorm_indicator_eq_indicator_enorm :
Expand Down
2 changes: 1 addition & 1 deletion Mathlib/Analysis/Normed/Group/InfiniteSum.lean
Original file line number Diff line number Diff line change
Expand Up @@ -41,7 +41,7 @@ open Topology ENNReal NNReal
open Finset Filter Metric

variable {ι α E F ε : Type*} [SeminormedAddCommGroup E] [SeminormedAddCommGroup F]
[TopologicalSpace ε] [ESeminormedAddCommMonoid ε]
[TopologicalSpace ε] [AddCommMonoid ε] [ESeminormedAddMonoid ε]

theorem cauchySeq_finset_iff_vanishing_norm {f : ι → E} :
(CauchySeq fun s : Finset ι => ∑ i ∈ s, f i) ↔
Expand Down
4 changes: 2 additions & 2 deletions Mathlib/Analysis/Normed/Group/Real.lean
Original file line number Diff line number Diff line change
Expand Up @@ -39,7 +39,7 @@ instance : ENorm ℝ≥0∞ where

@[simp] lemma enorm_eq_self (x : ℝ≥0∞) : ‖x‖ₑ = x := rfl

noncomputable instance : ENormedAddCommMonoid ℝ≥0∞ where
noncomputable instance : ENormedAddMonoid ℝ≥0∞ where
continuous_enorm := continuous_id
enorm_zero := by simp
enorm_eq_zero := by simp
Expand Down Expand Up @@ -120,7 +120,7 @@ end Real
section SeminormedCommGroup

variable [SeminormedCommGroup E] [SeminormedCommGroup F] {a b : E} {r : ℝ}
variable {ε : Type*} [TopologicalSpace ε] [ESeminormedCommMonoid ε]
variable {ε : Type*} [TopologicalSpace ε] [CommMonoid ε] [ESeminormedMonoid ε]

@[to_additive (attr := simp high) norm_norm] -- Higher priority as a shortcut lemma.
lemma norm_norm' (x : E) : ‖‖x‖‖ = ‖x‖ := Real.norm_of_nonneg (norm_nonneg' _)
Expand Down
2 changes: 1 addition & 1 deletion Mathlib/MeasureTheory/Function/L1Space/AEEqFun.lean
Original file line number Diff line number Diff line change
Expand Up @@ -35,7 +35,7 @@ open EMetric ENNReal Filter MeasureTheory NNReal Set

variable {α β ε ε' : Type*} {m : MeasurableSpace α} {μ ν : Measure α}
variable [NormedAddCommGroup β] [TopologicalSpace ε] [ContinuousENorm ε]
[TopologicalSpace ε'] [ESeminormedAddMonoid ε']
[TopologicalSpace ε'] [AddMonoid ε'] [ESeminormedAddMonoid ε']

namespace MeasureTheory

Expand Down
10 changes: 6 additions & 4 deletions Mathlib/MeasureTheory/Function/L1Space/HasFiniteIntegral.lean
Original file line number Diff line number Diff line change
Expand Up @@ -38,7 +38,7 @@ open Set Filter TopologicalSpace ENNReal EMetric MeasureTheory

variable {α β γ ε ε' ε'' : Type*} {m : MeasurableSpace α} {μ ν : Measure α}
variable [NormedAddCommGroup β] [NormedAddCommGroup γ] [ENorm ε] [ENorm ε']
[TopologicalSpace ε''] [ESeminormedAddMonoid ε'']
[TopologicalSpace ε''] [AddMonoid ε''] [ESeminormedAddMonoid ε'']

namespace MeasureTheory

Expand Down Expand Up @@ -246,7 +246,8 @@ theorem hasFiniteIntegral_zero_measure {m : MeasurableSpace α} (f : α → ε)

variable (α μ) in
@[fun_prop, simp]
theorem hasFiniteIntegral_zero {ε : Type*} [TopologicalSpace ε] [ESeminormedAddMonoid ε] :
theorem hasFiniteIntegral_zero {ε : Type*}
[TopologicalSpace ε] [AddMonoid ε] [ESeminormedAddMonoid ε] :
HasFiniteIntegral (fun _ : α => (0 : ε)) μ := by
simp [hasFiniteIntegral_iff_enorm]

Expand Down Expand Up @@ -284,7 +285,8 @@ theorem HasFiniteIntegral.of_isEmpty [IsEmpty α] {f : α → β} :

@[simp]
theorem HasFiniteIntegral.of_subsingleton_codomain
{ε : Type*} [TopologicalSpace ε] [ESeminormedAddMonoid ε] [Subsingleton ε] {f : α → ε} :
{ε : Type*} [TopologicalSpace ε] [AddMonoid ε] [ESeminormedAddMonoid ε]
[Subsingleton ε] {f : α → ε} :
HasFiniteIntegral f μ :=
hasFiniteIntegral_zero _ _ |>.congr <| .of_forall fun _ ↦ Subsingleton.elim _ _

Expand Down Expand Up @@ -313,7 +315,7 @@ theorem isFiniteMeasure_withDensity_ofReal {f : α → ℝ} (hfi : HasFiniteInte
section DominatedConvergence

variable {F : ℕ → α → β} {f : α → β} {bound : α → ℝ}
{ε : Type*} [TopologicalSpace ε] [ESeminormedAddMonoid ε]
{ε : Type*} [TopologicalSpace ε] [AddMonoid ε] [ESeminormedAddMonoid ε]
{F' : ℕ → α → ε} {f' : α → ε} {bound' : α → ℝ≥0∞}

theorem all_ae_norm_ofReal_F_le_bound (h : ∀ n, ∀ᵐ a ∂μ, ‖F n a‖ ≤ bound a) :
Expand Down
12 changes: 7 additions & 5 deletions Mathlib/MeasureTheory/Function/L1Space/Integrable.lean
Original file line number Diff line number Diff line change
Expand Up @@ -247,7 +247,8 @@ lemma integrable_norm_pow_of_le [IsFiniteMeasure μ] {f : α → β} (hf : AEStr
theorem Integrable.mono_measure {f : α → ε} (h : Integrable f ν) (hμ : μ ≤ ν) : Integrable f μ :=
⟨h.aestronglyMeasurable.mono_measure hμ, h.hasFiniteIntegral.mono_measure hμ⟩

theorem Integrable.of_measure_le_smul {ε} [TopologicalSpace ε] [ESeminormedAddMonoid ε]
theorem Integrable.of_measure_le_smul {ε}
[TopologicalSpace ε] [AddMonoid ε] [ESeminormedAddMonoid ε]
{μ' : Measure α} {c : ℝ≥0∞} (hc : c ≠ ∞) (hμ'_le : μ' ≤ c • μ)
{f : α → ε} (hf : Integrable f μ) : Integrable f μ' := by
rw [← memLp_one_iff_integrable] at hf ⊢
Expand Down Expand Up @@ -305,7 +306,7 @@ theorem integrable_finset_sum_measure [PseudoMetrizableSpace ε]

section

variable {ε : Type*} [TopologicalSpace ε] [ESeminormedAddMonoid ε]
variable {ε : Type*} [TopologicalSpace ε] [AddMonoid ε] [ESeminormedAddMonoid ε]

@[fun_prop]
theorem Integrable.smul_measure {f : α → ε} (h : Integrable f μ) {c : ℝ≥0∞} (hc : c ≠ ∞) :
Expand Down Expand Up @@ -399,7 +400,7 @@ theorem lintegral_edist_lt_top {f g : α → β} (hf : Integrable f μ) (hg : In

section ESeminormedAddMonoid

variable {ε' : Type*} [TopologicalSpace ε'] [ESeminormedAddMonoid ε']
variable {ε' : Type*} [TopologicalSpace ε'] [AddMonoid ε'] [ESeminormedAddMonoid ε']

variable (α ε') in
@[simp]
Expand Down Expand Up @@ -430,7 +431,8 @@ end ESeminormedAddMonoid

section ESeminormedAddCommMonoid

variable {ε' : Type*} [TopologicalSpace ε'] [ESeminormedAddCommMonoid ε'] [ContinuousAdd ε']
variable {ε' : Type*} [TopologicalSpace ε'] [AddCommMonoid ε'] [ESeminormedAddMonoid ε']
[ContinuousAdd ε']

@[fun_prop]
theorem integrable_finset_sum' {ι} (s : Finset ι) {f : ι → α → ε'}
Expand Down Expand Up @@ -950,7 +952,7 @@ end PosPart
section IsBoundedSMul

variable {𝕜 : Type*}
{ε : Type*} [TopologicalSpace ε] [ESeminormedAddMonoid ε]
{ε : Type*} [TopologicalSpace ε] [AddMonoid ε] [ESeminormedAddMonoid ε]

@[to_fun (attr := fun_prop)]
theorem Integrable.smul [NormedAddCommGroup 𝕜] [SMulZeroClass 𝕜 β] [IsBoundedSMul 𝕜 β] (c : 𝕜)
Expand Down
6 changes: 3 additions & 3 deletions Mathlib/MeasureTheory/Function/LocallyIntegrable.lean
Original file line number Diff line number Diff line change
Expand Up @@ -33,7 +33,7 @@ open scoped Topology Interval ENNReal
variable {X Y ε ε' ε'' E F R : Type*} [MeasurableSpace X] [TopologicalSpace X]
variable [MeasurableSpace Y] [TopologicalSpace Y]
variable [TopologicalSpace ε] [ContinuousENorm ε] [TopologicalSpace ε'] [ContinuousENorm ε']
[TopologicalSpace ε''] [ESeminormedAddMonoid ε'']
[TopologicalSpace ε''] [AddMonoid ε''] [ESeminormedAddMonoid ε'']
[NormedAddCommGroup E] [NormedAddCommGroup F] {f g : X → ε} {μ ν : Measure X} {s : Set X}

namespace MeasureTheory
Expand Down Expand Up @@ -397,14 +397,14 @@ protected theorem LocallyIntegrable.smul {f : X → E} {𝕜 : Type*} [NormedAdd
[SMulZeroClass 𝕜 E] [IsBoundedSMul 𝕜 E] (hf : LocallyIntegrable f μ) (c : 𝕜) :
LocallyIntegrable (c • f) μ := fun x ↦ (hf x).smul c

variable {ε''' : Type*} [TopologicalSpace ε'''] [ESeminormedAddCommMonoid ε''']
variable {ε''' : Type*} [TopologicalSpace ε'''] [AddCommMonoid ε'''] [ESeminormedAddMonoid ε''']
[ContinuousAdd ε'''] in
theorem locallyIntegrable_finset_sum' {ι} (s : Finset ι) {f : ι → X → ε'''}
(hf : ∀ i ∈ s, LocallyIntegrable (f i) μ) : LocallyIntegrable (∑ i ∈ s, f i) μ :=
Finset.sum_induction f (fun g => LocallyIntegrable g μ) (fun _ _ => LocallyIntegrable.add)
locallyIntegrable_zero hf

variable {ε''' : Type*} [TopologicalSpace ε'''] [ESeminormedAddCommMonoid ε''']
variable {ε''' : Type*} [TopologicalSpace ε'''] [AddCommMonoid ε'''] [ESeminormedAddMonoid ε''']
[ContinuousAdd ε'''] in
theorem locallyIntegrable_finset_sum {ι} (s : Finset ι) {f : ι → X → ε'''}
(hf : ∀ i ∈ s, LocallyIntegrable (f i) μ) : LocallyIntegrable (fun a ↦ ∑ i ∈ s, f i a) μ := by
Expand Down
12 changes: 6 additions & 6 deletions Mathlib/MeasureTheory/Function/LpSeminorm/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -77,7 +77,7 @@ theorem memLp_zero_iff_aestronglyMeasurable [TopologicalSpace ε] {f : α → ε

section ESeminormedAddMonoid

variable {ε : Type*} [TopologicalSpace ε] [ESeminormedAddMonoid ε]
variable {ε : Type*} [TopologicalSpace ε] [AddMonoid ε] [ESeminormedAddMonoid ε]

@[simp]
theorem eLpNorm'_zero (hp0_lt : 0 < q) : eLpNorm' (0 : α → ε) q μ = 0 := by
Expand Down Expand Up @@ -175,7 +175,7 @@ end Neg
section Const

variable {ε' ε'' : Type*} [TopologicalSpace ε'] [ContinuousENorm ε']
[TopologicalSpace ε''] [ESeminormedAddMonoid ε'']
[TopologicalSpace ε''] [AddMonoid ε''] [ESeminormedAddMonoid ε'']

theorem eLpNorm'_const (c : ε) (hq_pos : 0 < q) :
eLpNorm' (fun _ : α => c) q μ = ‖c‖ₑ * μ Set.univ ^ (1 / q) := by
Expand Down Expand Up @@ -388,7 +388,7 @@ theorem eLpNormEssSup_lt_top_of_ae_bound {f : α → F} {C : ℝ} (hfC : ∀ᵐ
eLpNormEssSup f μ < ∞ :=
(eLpNormEssSup_le_of_ae_bound hfC).trans_lt ENNReal.ofReal_lt_top

theorem eLpNorm_le_of_ae_enorm_bound {ε} [TopologicalSpace ε] [ESeminormedAddMonoid ε]
theorem eLpNorm_le_of_ae_enorm_bound {ε} [TopologicalSpace ε] [AddMonoid ε] [ESeminormedAddMonoid ε]
{f : α → ε} {C : ℝ≥0∞} (hfC : ∀ᵐ x ∂μ, ‖f x‖ₑ ≤ C) :
eLpNorm f p μ ≤ C • μ Set.univ ^ p.toReal⁻¹ := by
rcases eq_zero_or_neZero μ with rfl | hμ
Expand Down Expand Up @@ -602,7 +602,7 @@ end ContinuousENorm

section ENormedAddMonoid

variable {ε : Type*} [TopologicalSpace ε] [ENormedAddMonoid ε]
variable {ε : Type*} [TopologicalSpace ε] [AddMonoid ε] [ENormedAddMonoid ε]

/-- For a function `f` with support in `s`, the Lᵖ norms of `f` with respect to `μ` and
`μ.restrict s` are the same. -/
Expand Down Expand Up @@ -759,7 +759,7 @@ end ContinuousENorm

section ESeminormedAddMonoid

variable {ε : Type*} [TopologicalSpace ε] [ESeminormedAddMonoid ε]
variable {ε : Type*} [TopologicalSpace ε] [AddMonoid ε] [ESeminormedAddMonoid ε]

theorem eLpNorm'_eq_zero_of_ae_zero {f : α → ε} (hq0_lt : 0 < q) (hf_zero : f =ᵐ[μ] 0) :
eLpNorm' f q μ = 0 := by rw [eLpNorm'_congr_ae hf_zero, eLpNorm'_zero hq0_lt]
Expand Down Expand Up @@ -816,7 +816,7 @@ end ESeminormedAddMonoid

section ENormedAddMonoid

variable {ε : Type*} [TopologicalSpace ε] [ENormedAddMonoid ε]
variable {ε : Type*} [TopologicalSpace ε] [AddMonoid ε] [ENormedAddMonoid ε]

theorem ae_eq_zero_of_eLpNorm'_eq_zero {f : α → ε} (hq0 : 0 ≤ q) (hf : AEStronglyMeasurable f μ)
(h : eLpNorm' f q μ = 0) : f =ᵐ[μ] 0 := by
Expand Down
2 changes: 1 addition & 1 deletion Mathlib/MeasureTheory/Function/LpSeminorm/CompareExp.lean
Original file line number Diff line number Diff line change
Expand Up @@ -28,7 +28,7 @@ section SameSpace

variable {α ε ε' : Type*} {m : MeasurableSpace α} {μ : Measure α} {f : α → ε}
[TopologicalSpace ε] [ContinuousENorm ε]
[TopologicalSpace ε'] [ESeminormedAddMonoid ε']
[TopologicalSpace ε'] [AddMonoid ε'] [ESeminormedAddMonoid ε']

theorem eLpNorm'_le_eLpNorm'_mul_rpow_measure_univ {p q : ℝ} (hp0_lt : 0 < p) (hpq : p ≤ q)
(hf : AEStronglyMeasurable f μ) :
Expand Down
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