Theorems · Theorem · measure theory

mem_map_indicator_ae_iff_mem_map_restrict_ae_of_zero_mem

∀ {α : Type u_2} {β : Type u_3} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} {s : Set α} {f : α → β}
  [inst_1 : Zero β] {t : Set β},
  0 ∈ t →
    MeasurableSet s →
      (t ∈ Filter.map (s.indicator f) (MeasureTheory.ae μ) ↔ t ∈ Filter.map f (MeasureTheory.ae (μ.restrict s)))

Defined in

Mathlib.MeasureTheory.Measure.Restrict

Cited by

1 results in Mathlib

Foundations

Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceZero