Theorems · Theorem · measure theory

MeasureTheory.Measure.eqOn_of_ae_eq

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] {m : MeasurableSpace X} [inst_1 : TopologicalSpace Y]
  [T2Space Y] {μ : MeasureTheory.Measure X} [μ.IsOpenPosMeasure] {s : Set X} {f g : X → Y},
  f =ᵐ[μ.restrict s] g → ContinuousOn f s → ContinuousOn g s → s ⊆ closure (interior s) → Set.EqOn f g s

Defined in: Mathlib.MeasureTheory.Measure.OpenPos
Cited by: 4 results in Mathlib
Foundations: Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace TopologicalSpace T2Space MeasureTheory.Measure.IsOpenPosMeasure

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Cites19

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement and proof · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
MeasureTheory.aestatement and proof · cited by 2,352
Filter.EventuallyEqstatement and proof · cited by 1,912
MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
ContinuousOnstatement and proof · cited by 1,411
T2Spacestatement and proof · cited by 1,351
closurestatement and proof · cited by 1,254
interiorstatement and proof · cited by 714
Set.EqOnstatement · cited by 603

Cited by4

Results whose statement or proof uses this declaration.

MeasureTheory.Measure.eqOn_Icc_of_ae_eqproof · cited by 1
MeasureTheory.Measure.eqOn_Ico_of_ae_eqproof · cited by 0
MeasureTheory.Measure.eqOn_Ioc_of_ae_eqproof · cited by 0
MeasureTheory.Measure.eqOn_Ioo_of_ae_eqproof · cited by 0