Theorems · Theorem · measure theory

mem_map_indicator_ae_iff_of_zero_notMem

∀ {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 → (t ∈ Filter.map (s.indicator f) (MeasureTheory.ae μ) ↔ μ ((f ⁻¹' t)ᶜ ∪ sᶜ) = 0)

Defined in

Mathlib.MeasureTheory.Measure.Restrict

Cited by

1 results in Mathlib

Foundations

Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceZero