Theorems · Theorem · measure theory

MeasureTheory.lintegral_map_equiv

∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β] {μ : MeasureTheory.Measure α}
  (f : β → ENNReal) (g : α ≃ᵐ β), ∫⁻ (a : β), f a ∂MeasureTheory.Measure.map (⇑g) μ = ∫⁻ (a : α), f (g a) ∂μ

The lintegral transforms appropriately under a measurable equivalence g : α ≃ᵐ β. (Compare lintegral_map, which applies to a wider class of functions g : α → β, but requires measurability of the function being integrated.)

Defined in

Mathlib.MeasureTheory.Integral.Lebesgue.Map

Cited by

10 results in Mathlib

Foundations

Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpace