Theorems · Theorem · measure theory

MeasureTheory.Measure.prod_restrict

∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β] {μ : MeasureTheory.Measure α}
  {ν : MeasureTheory.Measure β} [MeasureTheory.SFinite ν] [MeasureTheory.SFinite μ] (s : Set α) (t : Set β),
  (μ.restrict s).prod (ν.restrict t) = (μ.prod ν).restrict (s ×ˢ t)

Defined in

Mathlib.MeasureTheory.Measure.Prod

Cited by

12 results in Mathlib

Foundations

Depth 222 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpaceMeasureTheory.SFiniteMeasureTheory.SFinite