Theorems · Theorem · functional analysis
toReal_enorm
∀ {E : Type u_5} [inst : SeminormedAddGroup E] (x : E), ‖x‖ₑ.toReal = ‖x‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 20 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- ENNReal.toRealstatement · cited by 859
- ENorm.enormstatement · cited by 715
- SeminormedAddGroupstatement and proof · cited by 331
Cited by20
Results whose statement or proof uses this declaration.
- ProbabilityTheory.variance_eq_integralproof · cited by 10
- MeasureTheory.enorm_setToFun_leproof · cited by 4
- MeasureTheory.norm_indicatorConstLpproof · cited by 4
- MeasureTheory.lpNorm_eq_integral_norm_rpow_toRealproof · cited by 3
- MeasureTheory.VectorMeasure.norm_measure_le_variationproof · cited by 2
- MeasureTheory.Integrable.summable_integralproof · cited by 2
- ProbabilityTheory.IndepFun.integral_bilin_comp_comp'proof · cited by 2
- MeasureTheory.norm_indicatorConstLp_topproof · cited by 1
- ProbabilityTheory.IndepFun.integrable_bilinproof · cited by 1
- MeasureTheory.lpNorm_constproof · cited by 1
- MeasureTheory.lpNorm_const'proof · cited by 1
- MeasureTheory.lpNorm_const_smulproof · cited by 1