Theorems · Definition · measure theory
Set.indicator
{α : Type u_1} → {M : Type u_3} → [Zero M] → Set α → (α → M) → α → MSet.indicator s f a is f a if a ∈ s, 0 otherwise.
- Defined in
- Mathlib.Algebra.Notation.Indicator
- Cited by
- 723 results in Mathlib
- Foundations
- Depth 13 from the axioms, rests on 62 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- Zero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
Cited by748
Results whose statement or proof uses this declaration.
- Summable.hasSumproof · cited by 184
- Set.indicator_of_memstatement · cited by 161
- Set.indicator_of_notMemstatement · cited by 154
- MeasureTheory.indicatorConstLpproof · cited by 64
- tsum_zeroproof · cited by 63
- SmoothBumpFunction.toFunproof · cited by 53
- Set.indicator_applystatement · cited by 48
- MeasureTheory.lintegral_indicatorstatement and proof · cited by 47
- MeasureTheory.Measure.dirac_apply'statement · cited by 43
- MeasureTheory.integral_indicatorstatement and proof · cited by 38
- Measurable.indicatorstatement · cited by 38
- MeasureTheory.UnifIntegrableproof · cited by 31
Showing the 200 most cited of 748.