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Theorems · Theorem · measure theory

MeasureTheory.Measure.prod_zero

∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β] (μ : MeasureTheory.Measure α),
  μ.prod 0 = 0
Defined in
Mathlib.MeasureTheory.Measure.Prod
Cited by
3 results in Mathlib
Foundations
Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasurableSpaceMeasurableSpace
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Around this declaration

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

ProbabilityTheory.Kernel.parallelComp_zero_right · cited by 1Kernel.parallelComp_zero_…MeasureTheory.Measure.mconv_zero · cited by 0Measure.mconv_zeroMeasureTheory.Measure.conv_zero · cited by 0Measure.conv_zeroDFunLike.coe · cited by 62936DFunLike.coeMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureSet.univ · cited by 3945Set.univsmul_zero · cited by 665smul_zeroMeasureTheory.Measure.prod · cited by 353Measure.prodMeasureTheory.Measure.bind · cited by 173Measure.bindMeasureTheory.Measure.map_zero · cited by 17Measure.map_zeroMeasureTheory.Measure.prod_def · cited by 6Measure.prod_defMeasureTheory.Measure.bind_const · cited by 3Measure.bind_constMeasure.prod_zeroCITED BYCITES

Cites10

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

Cited by3

Results whose statement or proof uses this declaration.