Theorems · Theorem · probability

ProbabilityTheory.posterior_boolKernel_apply_false

∀ {𝓧 : Type u_2} {m𝓧 : MeasurableSpace 𝓧} (μ ν : MeasureTheory.Measure 𝓧) [inst : MeasureTheory.IsFiniteMeasure μ]
  [inst_1 : MeasureTheory.IsFiniteMeasure ν] (π : MeasureTheory.Measure Bool)
  [inst_2 : MeasureTheory.IsFiniteMeasure π],
  ∀ᵐ (x : 𝓧) ∂π.bind ⇑(ProbabilityTheory.Kernel.boolKernel μ ν),
    ((ProbabilityTheory.posterior (ProbabilityTheory.Kernel.boolKernel μ ν) π) x) {false} =
      π {false} * μ.rnDeriv (π.bind ⇑(ProbabilityTheory.Kernel.boolKernel μ ν)) x

Defined in

Mathlib.Probability.Kernel.Posterior

Cited by

0 results in Mathlib

Foundations

Depth 342 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.IsFiniteMeasureMeasureTheory.IsFiniteMeasureMeasureTheory.IsFiniteMeasure