Theorems · Theorem · functional analysis
nnnorm_indicator_eq_indicator_nnnorm
∀ {α : Type u_1} {E : Type u_2} [inst : SeminormedAddGroup E] {s : Set α} (f : α → E) (a : α),
‖s.indicator f a‖₊ = s.indicator (fun a => ‖f a‖₊) a- Defined in
- Mathlib.Analysis.Normed.Group.Indicator
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 115 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
- NNRealstatement · cited by 4,310
- NNNorm.nnnormstatement · cited by 952
- Set.indicatorstatement · cited by 723
- SeminormedAddGroupstatement and proof · cited by 331
- nnnorm_zeroproof · cited by 40
- Set.indicator_comp_of_zeroproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.uniformIntegrable_of'proof · cited by 2
- MeasureTheory.UniformIntegrable.spec'proof · cited by 1