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Theorems · Theorem · measure theory

MeasureTheory.AEStronglyMeasurable.prodMk

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : TopologicalSpace β] [inst_1 : TopologicalSpace γ]
  {m m₀ : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → β} {g : α → γ},
  MeasureTheory.AEStronglyMeasurable f μ →
    MeasureTheory.AEStronglyMeasurable g μ → MeasureTheory.AEStronglyMeasurable (fun x => (f x, g x)) μ
Defined in
Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable
Cited by
18 results in Mathlib
Foundations
Depth 174 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.smul · cited by 14AEStronglyMeasurable.smulMeasureTheory.AEEqFun.coeFn_comp₂ · cited by 6AEEqFun.coeFn_comp₂MeasureTheory.AEStronglyMeasurable.inner · cited by 6AEStronglyMeasurable.innerMeasureTheory.Integrable.prodMk · cited by 5Integrable.prodMkContinuous.comp_aestronglyMeasurable₂ · cited by 5Continuous.comp_aestrongl…MeasureTheory.AEEqFun.pair_eq_mk · cited by 3AEEqFun.pair_eq_mkVectorFourier.integral_fourierIntegral_swap · cited by 2VectorFourier.integral_fo…MeasureTheory.AEStronglyMeasurable.fourierSMulRight · cited by 2AEStronglyMeasurable.four…MeasureTheory.AEStronglyMeasurable.vadd · cited by 1AEStronglyMeasurable.vaddMeasureTheory.AEStronglyMeasurable.edist · cited by 1AEStronglyMeasurable.edistMeasureTheory.AEEqFun.comp₂Measurable_eq_mk · cited by 1AEEqFun.comp₂Measurable_e…MeasureTheory.AEEqFun.comp₂_eq_mk · cited by 1AEEqFun.comp₂_eq_mkMeasureTheory.AEStronglyMeasurable.vadd_const · cited by 0AEStronglyMeasurable.vadd…MeasureTheory.AEEqFun.coeFn_pair · cited by 0AEEqFun.coeFn_pairMeasureTheory.AEEqFun.pair_mk_mk · cited by 0AEEqFun.pair_mk_mkTopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasureTheory.AEStronglyMeasurable · cited by 755MeasureTheory.AEStronglyM…MeasureTheory.AEStronglyMeasurable.mk · cited by 82AEStronglyMeasurable.mkMeasureTheory.AEStronglyMeasurable.ae_eq_mk · cited by 77AEStronglyMeasurable.ae_e…MeasureTheory.AEStronglyMeasurable.stronglyMeasurable_mk · cited by 71AEStronglyMeasurable.stro…MeasureTheory.StronglyMeasurable.prodMk · cited by 11StronglyMeasurable.prodMkFilter.EventuallyEq.prodMk · cited by 4EventuallyEq.prodMkAEStronglyMeasurable.prodMkCITED BYCITES

Cites9

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Cited by18

Results whose statement or proof uses this declaration.