Theorems · Theorem · functional analysis
norm_indicator_le_of_subset
∀ {α : Type u_1} {E : Type u_2} [inst : SeminormedAddGroup E] {s t : Set α},
s ⊆ t → ∀ (f : α → E) (a : α), ‖s.indicator f a‖ ≤ ‖t.indicator f a‖- Defined in
- Mathlib.Analysis.Normed.Group.Indicator
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- le_reflproof · cited by 2,061
- norm_nonnegproof · cited by 725
- Set.indicatorstatement and proof · cited by 723
- le_imp_le_of_le_of_leproof · cited by 576
- SeminormedAddGroupstatement and proof · cited by 331
- Set.indicator_le_indicator_apply_of_subsetproof · cited by 12
- norm_indicator_eq_indicator_normproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.UnifTight.eventually_cofinite_indicatorproof · cited by 2
- MeasureTheory.unifIntegrable_of'proof · cited by 1