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Theorems · Theorem · measure theory

Set.indicator_eq_zero

∀ {α : Type u_1} {M : Type u_3} [inst : Zero M] {s : Set α} {f : α → M},
  (s.indicator f = fun x => 0) ↔ Disjoint (Function.support f) s
Defined in
Mathlib.Algebra.Notation.Indicator
Cited by
3 results in Mathlib
Foundations
Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Zero
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.indicator_empty · cited by 6Set.indicator_emptySet.indicator_zero · cited by 4Set.indicator_zeroSet.indicator_eq_zero' · cited by 1Set.indicator_eq_zero'Set · cited by 53352SetDisjoint · cited by 2201DisjointSet.indicator · cited by 723Set.indicatorFunction.support · cited by 610Function.supportSet.disjoint_left · cited by 121Set.disjoint_leftnot_imp_not · cited by 63not_imp_notFunction.mem_support · cited by 54Function.mem_supportSet.indicator_apply_eq_zero · cited by 8Set.indicator_apply_eq_ze…Set.indicator_eq_zeroCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.