Theorems · Theorem · probability

ProbabilityTheory.Kernel.withDensity_add_right

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {κ : ProbabilityTheory.Kernel α β}
  [inst : ProbabilityTheory.IsSFiniteKernel κ] {f g : α → β → ENNReal},
  Measurable (Function.uncurry f) →
    Measurable (Function.uncurry g) → κ.withDensity (f + g) = κ.withDensity f + κ.withDensity g

Defined in: Mathlib.Probability.Kernel.WithDensity
Cited by: 1 results in Mathlib
Foundations: Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: ProbabilityTheory.IsSFiniteKernel

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Cites22

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.Measureproof · cited by 10,939
ENNRealstatement and proof · cited by 9,879
MeasurableSetproof · cited by 3,075
Measurablestatement and proof · cited by 1,499
ProbabilityTheory.Kernelstatement and proof · cited by 1,281
MeasureTheory.Measure.extproof · cited by 308
MeasureTheory.Measure.withDensityproof · cited by 265
ProbabilityTheory.IsSFiniteKernelstatement and proof · cited by 248
measurable_constproof · cited by 156

Cited by1

Results whose statement or proof uses this declaration.

ProbabilityTheory.Kernel.withDensity_sub_add_cancelproof · cited by 1