Theorems · Theorem · measure theory

MeasureTheory.NullMeasurableSet.right_of_prod

∀ {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] {s : Set α} {t : Set β},
  MeasureTheory.NullMeasurableSet (s ×ˢ t) (μ.prod ν) → μ s ≠ 0 → MeasureTheory.NullMeasurableSet t ν

If s ×ˢ t is a null measurable set and μ s ≠ 0, then t is a null measurable set.

Defined in

Mathlib.MeasureTheory.Measure.Prod

Cited by

3 results in Mathlib

Foundations

Depth 220 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpaceMeasureTheory.SFinite