Theorems · Theorem · measure theory

Set.indicator_const_preimage_eq_union

∀ {α : Type u_1} {M : Type u_3} [inst : Zero M] (U : Set α) (s : Set M) (a : M) [inst_1 : Decidable (a ∈ s)]
  [inst_2 : Decidable (0 ∈ s)], (U.indicator fun x => a) ⁻¹' s = (if a ∈ s then U else ∅) ∪ if 0 ∈ s then Uᶜ else ∅

Defined in

Mathlib.Algebra.Notation.Indicator

Cited by

3 results in Mathlib

Foundations

Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ZeroDecidableDecidable