Theorems · Theorem · probability

MeasureTheory.Measure.compProd_const

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {μ : MeasureTheory.Measure α}
  {ν : MeasureTheory.Measure β} [MeasureTheory.SFinite μ] [MeasureTheory.SFinite ν],
  μ.compProd (ProbabilityTheory.Kernel.const α ν) = μ.prod ν

The composition product of a measure and a constant kernel is the product between the two measures.

Defined in: Mathlib.Probability.Kernel.Composition.MeasureCompProd
Cited by: 4 results in Mathlib
Foundations: Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasureTheory.SFinite MeasureTheory.SFinite

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Cites16

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

DFunLike.coeproof · cited by 62,936
Setproof · cited by 53,352
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
Set.preimageproof · cited by 4,946
MeasurableSetproof · cited by 3,075
ProbabilityTheory.Kernelproof · cited by 1,281
MeasureTheory.lintegralproof · cited by 1,152
MeasureTheory.SFinitestatement and proof · cited by 449
MeasureTheory.Measure.prodstatement and proof · cited by 353
MeasureTheory.Measure.extproof · cited by 308
ProbabilityTheory.IsSFiniteKernelproof · cited by 248

Cited by4

Results whose statement or proof uses this declaration.

ProbabilityTheory.absolutelyContinuous_posteriorproof · cited by 4
MeasureTheory.Measure.isProjectiveLimit_infinitePiNatproof · cited by 1
ProbabilityTheory.absolutelyContinuous_of_posteriorproof · cited by 1
MeasureTheory.Measure.snd_dirac_unit_compProd_constproof · cited by 0