Theorems · Definition · measure theory

MeasureTheory.Measure.bind

{α : Type u_1} →
  {β : Type u_2} →
    {mα : MeasurableSpace α} →
      {mβ : MeasurableSpace β} → MeasureTheory.Measure α → (α → MeasureTheory.Measure β) → MeasureTheory.Measure β

Monadic bind on Measure, only works in the category of measurable spaces and measurable functions. When the function f is not measurable the result is not well defined.

Defined in

Mathlib.MeasureTheory.Measure.GiryMonad

Cited by

173 results in Mathlib

Foundations

Depth 209 from the axioms, rests on 5,160 definitions · uses propext, Classical.choice, Quot.sound