Theorems · Theorem · group theory
Set.indicator_self_add_compl
∀ {α : Type u_1} {M : Type u_4} [inst : AddZeroClass M] (s : Set α) (f : α → M), s.indicator f + sᶜ.indicator f = f- Defined in
- Mathlib.Algebra.Group.Indicator
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddZeroClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Compl.complstatement · cited by 2,925
- AddZeroClassstatement and proof · cited by 1,237
- Set.indicatorstatement · cited by 723
- Set.indicator_self_add_compl_applyproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.condExp_indicatorproof · cited by 5
- MeasureTheory.tendsto_Lp_finite_of_tendsto_ae_of_measproof · cited by 1