Theorems · Theorem · measure theory

MeasureTheory.Measure.prod_sum

∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β] {ι : Type u_4} {ι' : Type u_5}
  [Countable ι'] (m : ι → MeasureTheory.Measure α) (m' : ι' → MeasureTheory.Measure β)
  [∀ (n : ι'), MeasureTheory.SFinite (m' n)],
  (MeasureTheory.Measure.sum m).prod (MeasureTheory.Measure.sum m') =
    MeasureTheory.Measure.sum fun p => (m p.1).prod (m' p.2)

Defined in

Mathlib.MeasureTheory.Measure.Prod

Cited by

6 results in Mathlib

Foundations

Depth 217 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpaceCountableMeasureTheory.SFinite