Theorems · Theorem · measure theory
Set.mulIndicator_of_mem
∀ {α : Type u_1} {M : Type u_3} [inst : One M] {s : Set α} {a : α}, a ∈ s → ∀ (f : α → M), s.mulIndicator f a = f a- Defined in
- Mathlib.Algebra.Notation.Indicator
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- One
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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.mulIndicatorstatement · cited by 163
Cited by25
Results whose statement or proof uses this declaration.
- Multipliable.hasProdproof · cited by 88
- Set.mulIndicator_apply_le'proof · cited by 5
- Finset.prod_mulIndicator_eq_prod_filterproof · cited by 4
- Set.apply_mulIndicator_symmDiffproof · cited by 2
- tprod_mulIndicator_of_disjoint_on_mulSupport_of_memproof · cited by 2
- tprod_subtypeproof · cited by 2
- Set.mulIndicator_self_mul_compl_applyproof · cited by 2
- Set.mulIndicator_union_mul_inter_applyproof · cited by 2
- Set.mulIndicator_comp_of_oneproof · cited by 2
- mulIndicator_eventuallyEqproof · cited by 2
- mulIndicator_iUnion_of_pairwise_disjoint_on_mulSupportproof · cited by 1
- mulIndicator_thickening_eventually_eq_mulIndicator_closureproof · cited by 1