Theorems · Theorem · measure theory

MeasureTheory.Measure.pi_nullSingletonClass

∀ {ι : Type u_1} {α : ι → Type u_3} [inst : Fintype ι] [inst_1 : (i : ι) → MeasurableSpace (α i)]
  {μ : (i : ι) → MeasureTheory.Measure (α i)} [∀ (i : ι), MeasureTheory.SigmaFinite (μ i)] (i : ι)
  [MeasureTheory.NullSingletonClass (μ i)], MeasureTheory.NullSingletonClass (MeasureTheory.Measure.pi μ)

If one of the measures μ i has value zero on singeltons, them Measure.pi µ has value zero on singletons. The instance below assumes that all μ i have value zero on singletons.

Defined in

Mathlib.MeasureTheory.Constructions.Pi

Cited by

1 results in Mathlib

Foundations

Depth 233 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeMeasurableSpaceMeasureTheory.SigmaFiniteMeasureTheory.NullSingletonClass