Theorems · Theorem · measure theory

MeasureTheory.SimpleFunc.lintegral_eq_of_measure_preimage

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : MeasurableSpace β]
  {f : MeasureTheory.SimpleFunc α ENNReal} {g : MeasureTheory.SimpleFunc β ENNReal} {ν : MeasureTheory.Measure β},
  (∀ (y : ENNReal), μ (⇑f ⁻¹' {y}) = ν (⇑g ⁻¹' {y})) → f.lintegral μ = g.lintegral ν

SimpleFunc.lintegral depends only on the measures of f ⁻¹' {y}.

Defined in

Mathlib.MeasureTheory.Function.SimpleFunc

Cited by

2 results in Mathlib

Foundations

Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace