Theorems · Theorem · measure theory

MeasureTheory.NullMeasurableSet.of_preimage_fst

∀ {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] [NeZero ν] {s : Set α},
  MeasureTheory.NullMeasurableSet (Prod.fst ⁻¹' s) (μ.prod ν) → MeasureTheory.NullMeasurableSet s μ

If Prod.fst ⁻¹' s is a null measurable set and ν ≠ 0, then s is a null measurable set.

Defined in

Mathlib.MeasureTheory.Measure.Prod

Cited by

1 results in Mathlib

Foundations

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

Assumes

MeasurableSpaceMeasurableSpaceMeasureTheory.SFiniteMeasureTheory.SFiniteNeZero