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Theorems · Theorem · measure theory

Continuous.comp_stronglyMeasurable

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {x : MeasurableSpace α} [inst : TopologicalSpace β]
  [inst_1 : TopologicalSpace γ] {g : β → γ} {f : α → β},
  Continuous g → MeasureTheory.StronglyMeasurable f → MeasureTheory.StronglyMeasurable fun x => g (f x)
Defined in
Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic
Cited by
18 results in Mathlib
Foundations
Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace

Around this declaration

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

Continuous.comp_aestronglyMeasurable · cited by 77Continuous.comp_aestrongl…MeasureTheory.StronglyMeasurable.enorm · cited by 19StronglyMeasurable.enormstronglyMeasurable_iff_measurable_separable · cited by 13stronglyMeasurable_iff_me…MeasureTheory.StronglyMeasurable.nnnorm · cited by 7StronglyMeasurable.nnnormMeasureTheory.StronglyMeasurable.norm · cited by 7StronglyMeasurable.normMeasureTheory.StronglyMeasurable.edist · cited by 3StronglyMeasurable.edistMeasureTheory.condExp_stronglyMeasurable_bilin_of_bound · cited by 3MeasureTheory.condExp_str…MeasureTheory.StronglyMeasurable.smul · cited by 3StronglyMeasurable.smulMeasureTheory.StronglyMeasurable.smul_const · cited by 3StronglyMeasurable.smul_c…MeasureTheory.StronglyMeasurable.vadd · cited by 1StronglyMeasurable.vaddStronglyMeasurable.apply_continuousLinearMap · cited by 1StronglyMeasurable.apply_…MeasureTheory.StronglyMeasurable.dist · cited by 0StronglyMeasurable.distMeasureTheory.StronglyMeasurable.fst · cited by 0StronglyMeasurable.fstMeasureTheory.StronglyMeasurable.real_toNNReal · cited by 0StronglyMeasurable.real_t…MeasureTheory.StronglyMeasurable.snd · cited by 0StronglyMeasurable.sndTopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceContinuous · cited by 2592ContinuousFilter.Tendsto.comp · cited by 560Tendsto.compMeasureTheory.StronglyMeasurable · cited by 363MeasureTheory.StronglyMea…Continuous.tendsto · cited by 206Continuous.tendstoMeasureTheory.SimpleFunc.map · cited by 54SimpleFunc.mapMeasureTheory.StronglyMeasurable.approx · cited by 40StronglyMeasurable.approxMeasureTheory.StronglyMeasurable.tendsto_approx · cited by 36StronglyMeasurable.tendst…Continuous.comp_stronglyMeasu…CITED BYCITES

Cites9

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Cited by18

Results whose statement or proof uses this declaration.