Theorems · Theorem · functional analysis
norm_indicator_le_norm_self
∀ {α : Type u_1} {E : Type u_2} [inst : SeminormedAddGroup E] {s : Set α} (f : α → E) (a : α), ‖s.indicator f a‖ ≤ ‖f a‖- Defined in
- Mathlib.Analysis.Normed.Group.Indicator
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 114 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.
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
- Realstatement and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- Set.indicatorstatement · cited by 723
- SeminormedAddGroupstatement and proof · cited by 331
- norm_indicator_eq_indicator_normproof · cited by 11
- indicator_norm_le_norm_selfproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.AECover.integral_tendsto_of_countably_generatedproof · cited by 7