Theorems · Theorem · order theory
Set.indicator_le
∀ {α : Type u_2} {M : Type u_3} [inst : AddMonoid M] [inst_1 : PartialOrder M] [CanonicallyOrderedAdd M] {s : Set α}
{f g : α → M}, (∀ a ∈ s, f a ≤ g a) → s.indicator f ≤ g- Defined in
- Mathlib.Algebra.Order.Group.Indicator
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- PartialOrderstatement and proof · cited by 6,410
- AddMonoidstatement and proof · cited by 2,864
- Set.indicatorstatement · cited by 723
- zero_leproof · cited by 382
- CanonicallyOrderedAddstatement and proof · cited by 229
- Set.indicator_le'proof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_eq_nnrealproof · cited by 6
- MeasureTheory.uniformIntegrable_of'proof · cited by 2
- bergelson'proof · cited by 1
- ProbabilityTheory.Kernel.trajContent_tendsto_zeroproof · cited by 1