Theorems · Theorem · probability

ProbabilityTheory.IdentDistrib.measure_mem_eq

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β]
  [inst_2 : MeasurableSpace γ] {μ : MeasureTheory.Measure α} {ν : MeasureTheory.Measure β} {f : α → γ} {g : β → γ},
  ProbabilityTheory.IdentDistrib f g μ ν → ∀ {s : Set γ}, MeasurableSet s → μ (f ⁻¹' s) = ν (g ⁻¹' s)

Defined in

Mathlib.Probability.IdentDistrib

Cited by

3 results in Mathlib

Foundations

Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpaceMeasurableSpace