Theorems · Theorem · functional analysis
enorm_indicator_eq_indicator_enorm
∀ {α : Type u_1} {ε : Type u_2} [inst : TopologicalSpace ε] [inst_1 : ESeminormedAddMonoid ε] {s : Set α} (f : α → ε)
(a : α), ‖s.indicator f a‖ₑ = s.indicator (fun a => ‖f a‖ₑ) a- Defined in
- Mathlib.Analysis.Normed.Group.Indicator
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
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
- TopologicalSpacestatement and proof · cited by 24,529
- ENNRealstatement · cited by 9,879
- Set.indicatorstatement · cited by 723
- ENorm.enormstatement · cited by 715
- ESeminormedAddMonoidstatement and proof · cited by 133
- enorm_zeroproof · cited by 44
- Set.indicator_comp_of_zeroproof · cited by 8
Cited by9
Results whose statement or proof uses this declaration.
- MeasureTheory.integrable_indicator_iffproof · cited by 30
- MeasureTheory.eLpNorm_indicator_eq_eLpNorm_restrictproof · cited by 8
- MeasureTheory.eLpNorm_indicator_leproof · cited by 4
- MeasureTheory.MemLp.eLpNorm_indicator_norm_ge_leproof · cited by 1
- MeasureTheory.eLpNormEssSup_indicator_leproof · cited by 1
- MeasureTheory.lintegral_enorm_condExp_indicatorproof · cited by 1
- enorm_indicator_le_of_subsetproof · cited by 1
- enorm_indicator_le_enorm_selfproof · cited by 0