Theorems · Theorem · measure theory
Set.indicator_apply
∀ {α : Type u_1} {M : Type u_3} [inst : Zero M] (s : Set α) (f : α → M) (a : α) [inst_1 : Decidable (a ∈ s)],
s.indicator f a = if a ∈ s then f a else 0- Defined in
- Mathlib.Algebra.Notation.Indicator
- Cited by
- 48 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- Set.indicatorstatement · cited by 723
- Classical.decPredproof · cited by 26
Cited by48
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.compProd_applyproof · cited by 31
- eq_affineCombination_of_mem_affineSpan_of_fintypeproof · cited by 14
- MeasureTheory.Measure.map_dirac'proof · cited by 12
- MeasureTheory.Measure.map_diracproof · cited by 7
- Set.indicator_singletonproof · cited by 6
- MeasureTheory.condExp_indicatorproof · cited by 5
- Set.indicator_eq_one_iff_memproof · cited by 4
- MeasureTheory.UnifIntegrable.ae_eqproof · cited by 4
- indicator_indepFun_pi_of_prod_bcfproof · cited by 4
- ProbabilityTheory.Kernel.compProd_restrictproof · cited by 4
- Finsupp.filter_eq_indicatorproof · cited by 3
- Affine.Simplex.centroid_eq_affineCombination_of_pointsWithCircumcenterproof · cited by 3