Theorems · Theorem · functional analysis
norm_indicator_eq_indicator_norm
∀ {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
- 11 results in Mathlib
- Foundations
- Depth 89 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 · cited by 25,697
- Norm.normstatement · cited by 5,413
- Set.indicatorstatement · cited by 723
- norm_zeroproof · cited by 366
- SeminormedAddGroupstatement and proof · cited by 331
- Set.indicator_comp_of_zeroproof · cited by 8
Cited by11
Results whose statement or proof uses this declaration.
- MeasureTheory.MemLp.eLpNorm_indicator_norm_ge_pos_leproof · cited by 2
- MeasureTheory.IntegrableOn.continuousWithinAt_Ici_primitive_Ioiproof · cited by 2
- norm_indicator_le_of_subsetproof · cited by 2
- ProbabilityTheory.MemLp.uniformIntegrable_of_identDistrib_auxproof · cited by 1
- MeasureTheory.MemLp.eLpNorm_indicator_le'proof · cited by 1
- MeasureTheory.IntegrableOn.continuousWithinAt_Iic_primitive_Iioproof · cited by 1
- MeasureTheory.BorelCantelli.process_difference_leproof · cited by 1
- MeasureTheory.unifIntegrable_ofproof · cited by 1
- MeasureTheory.unifIntegrable_of'proof · cited by 1
- norm_indicator_le_norm_selfproof · cited by 1
- Antitone.tendsto_setIntegralproof · cited by 0