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Theorems · Theorem · measure theory

MeasureTheory.StronglyMeasurable.prodMk

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {m : MeasurableSpace α} [inst : TopologicalSpace β]
  [inst_1 : TopologicalSpace γ] {f : α → β} {g : α → γ},
  MeasureTheory.StronglyMeasurable f →
    MeasureTheory.StronglyMeasurable g → MeasureTheory.StronglyMeasurable fun x => (f x, g x)
Defined in
Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic
Cited by
11 results in Mathlib
Foundations
Depth 87 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.

MeasureTheory.AEStronglyMeasurable.prodMk · cited by 18AEStronglyMeasurable.prod…MeasureTheory.StronglyMeasurable.measurableSet_le · cited by 9StronglyMeasurable.measur…MeasureTheory.StronglyMeasurable.measurableSet_eq_fun · cited by 3StronglyMeasurable.measur…MeasureTheory.StronglyMeasurable.smul · cited by 3StronglyMeasurable.smulMeasureTheory.StronglyMeasurable.smul_const · cited by 3StronglyMeasurable.smul_c…MeasureTheory.StronglyMeasurable.edist · cited by 3StronglyMeasurable.edistMeasureTheory.condExp_stronglyMeasurable_bilin_of_bound · cited by 3MeasureTheory.condExp_str…MeasureTheory.StronglyMeasurable.vadd · cited by 1StronglyMeasurable.vaddMeasureTheory.StronglyMeasurable.dist · cited by 0StronglyMeasurable.distMeasureTheory.StronglyMeasurable.inner · cited by 0StronglyMeasurable.innerMeasureTheory.StronglyMeasurable.vadd_const · cited by 0StronglyMeasurable.vadd_c…DFunLike.coe · cited by 62936DFunLike.coeTopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceFilter · cited by 8121FilterFilter.Tendsto · cited by 3814Filter.TendstoFilter.atTop · cited by 2405Filter.atTopMeasureTheory.StronglyMeasurable · cited by 363MeasureTheory.StronglyMea…nhds_prod_eq · cited by 84nhds_prod_eqMeasureTheory.StronglyMeasurable.approx · cited by 40StronglyMeasurable.approxMeasureTheory.StronglyMeasurable.tendsto_approx · cited by 36StronglyMeasurable.tendst…Filter.Tendsto.prodMk · cited by 35Tendsto.prodMkMeasureTheory.SimpleFunc.pair · cited by 16SimpleFunc.pairStronglyMeasurable.prodMkCITED BYCITES

Cites12

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

Cited by11

Results whose statement or proof uses this declaration.