Theorems · Theorem · measure theory

MeasureTheory.Measure.nullMeasurableSet_prod_of_ne_zero

∀ {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 s ≠ 0 →
    ν t ≠ 0 →
      (MeasureTheory.NullMeasurableSet (s ×ˢ t) (μ.prod ν) ↔
        MeasureTheory.NullMeasurableSet s μ ∧ MeasureTheory.NullMeasurableSet t ν)

The product of two non-null sets is null measurable if and only if both of them are null measurable.

Defined in

Mathlib.MeasureTheory.Measure.Prod

Cited by

0 results in Mathlib

Foundations

Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpaceMeasureTheory.SFiniteMeasureTheory.SFinite