Theorems · Theorem · measure theory

MeasureTheory.integral_subtype_comap

∀ {G : Type u_5} [inst : NormedAddCommGroup G] [inst_1 : NormedSpace ℝ G] {α : Type u_6} [inst_2 : MeasurableSpace α]
  {μ : MeasureTheory.Measure α} {s : Set α},
  MeasurableSet s → ∀ (f : α → G), ∫ (x : ↑s), f ↑x ∂MeasureTheory.Measure.comap Subtype.val μ = ∫ (x : α) in s, f x ∂μ

Defined in

Mathlib.MeasureTheory.Integral.Bochner.Basic

Cited by

5 results in Mathlib

Foundations

Depth 256 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasurableSpace