Theorems · Theorem · order theory
Set.indicator_le_indicator_nonneg
∀ {α : Type u_2} {M : Type u_3} [inst : Zero M] [inst_1 : LinearOrder M] (s : Set α) (f : α → M),
s.indicator f ≤ {a | 0 ≤ f a}.indicator f- Defined in
- Mathlib.Algebra.Order.Group.Indicator
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ZeroLinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- LinearOrderstatement and proof · cited by 8,572
- Set.ofPredstatement and proof · cited by 6,101
- LT.lt.leproof · cited by 2,189
- le_rflproof · cited by 1,558
- Set.indicatorstatement · cited by 723
- not_leproof · cited by 328
- Set.indicator_applyproof · cited by 48
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.setIntegral_le_nonnegproof · cited by 1
- Set.indicator_nonpos_le_indicatorproof · cited by 1