Theorems · Theorem · measure theory
Set.indicator_eq_self
∀ {α : Type u_1} {M : Type u_3} [inst : Zero M] {s : Set α} {f : α → M}, s.indicator f = f ↔ Function.support f ⊆ s- Defined in
- Mathlib.Algebra.Notation.Indicator
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Zero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Function.supportstatement · cited by 610
- not_imp_commproof · cited by 56
- Function.mem_supportproof · cited by 54
- Set.indicator_apply_eq_selfproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- Set.indicator_univproof · cited by 10
- Set.indicator_supportproof · cited by 6
- MeasureTheory.MemLp.mono_exponent_of_measure_support_ne_topproof · cited by 4
- MeasureTheory.eLpNorm_sub_le_of_dist_bddproof · cited by 1
- intervalIntegral.integral_eq_integral_of_support_subsetproof · cited by 0
- Set.indicator_eq_self_of_supersetproof · cited by 0