Mathlib Map

Theorems · Theorem · measure theory

MeasureTheory.Measure.InnerRegular.map_of_continuous

∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} [inst_1 : TopologicalSpace α]
  [BorelSpace α] [inst_3 : MeasurableSpace β] [inst_4 : TopologicalSpace β] [BorelSpace β] [h : μ.InnerRegular]
  {f : α → β}, Continuous f → (MeasureTheory.Measure.map f μ).InnerRegular
Defined in
Mathlib.MeasureTheory.Measure.Regular
Cited by
2 results in Mathlib
Foundations
Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasurableSpaceTopologicalSpaceBorelSpaceMeasurableSpaceTopologicalSpaceBorelSpaceMeasureTheory.Measure.InnerRegular
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.Measure.InnerRegular.map · cited by 1InnerRegular.mapMeasureTheory.Measure.exists_innerRegular_eq_of_isCompact · cited by 1Measure.exists_innerRegul…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasurableSet · cited by 3075MeasurableSetContinuous · cited by 2592ContinuousBorelSpace · cited by 1602BorelSpaceIsCompact · cited by 1282IsCompactMeasureTheory.Measure.map · cited by 858Measure.mapContinuous.measurable · cited by 181Continuous.measurableIsCompact.image · cited by 105IsCompact.imageMeasureTheory.Measure.InnerRegular · cited by 49Measure.InnerRegularContinuous.aemeasurable · cited by 21Continuous.aemeasurableMeasureTheory.Measure.InnerRegular.innerRegular · cited by 7InnerRegular.innerRegularMeasureTheory.Measure.InnerRegularWRT.map · cited by 2InnerRegularWRT.mapInnerRegular.map_of_continuousCITED BYCITES

Cites15

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

Cited by2

Results whose statement or proof uses this declaration.