Theorems · Theorem · measure theory

measurable_measure_prodMk_left_finite

∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β] {ν : MeasureTheory.Measure β}
  [MeasureTheory.IsFiniteMeasure ν] {s : Set (α × β)}, MeasurableSet s → Measurable fun x => ν (Prod.mk x ⁻¹' s)

If ν is a finite measure, and s ⊆ α × β is measurable, then x ↦ ν { y | (x, y) ∈ s } is a measurable function. measurable_measure_prodMk_left is strictly more general.

Defined in

Mathlib.MeasureTheory.Measure.Prod

Cited by

1 results in Mathlib

Foundations

Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpaceMeasureTheory.IsFiniteMeasure