Theorems · Theorem

PMF.toMeasure_bind_apply

∀ {α : Type u_1} {β : Type u_2} (p : PMF α) (f : α → PMF β) (s : Set β) [inst : MeasurableSpace β],
  MeasurableSet s → (p.bind f).toMeasure s = ∑' (a : α), p a * (f a).toMeasure s

The measure of a set under p.bind f is the sum over a : α of the probability of a under p times the measure of the set under f a.

Defined in

Mathlib.Probability.ProbabilityMassFunction.Monad

Cited by

0 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace