Theorems · Definition · functional analysis
MeasureTheory.eLpNormEssSup
{α : Type u_1} → {ε : Type u_2} → {m0 : MeasurableSpace α} → [ENorm ε] → (α → ε) → MeasureTheory.Measure α → ENNRealseminorm for ℒ∞, equal to the essential supremum of ‖f‖.
- Cited by
- 59 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ENorm
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- ENorm.enormproof · cited by 715
- ENormstatement and proof · cited by 155
- essSupproof · cited by 69
Cited by60
Results whose statement or proof uses this declaration.
- MeasureTheory.eLpNormproof · cited by 329
- MeasureTheory.eLpNorm_exponent_zeroproof · cited by 43
- MeasureTheory.eLpNorm_exponent_topstatement and proof · cited by 36
- MeasureTheory.eLpNorm_eq_eLpNorm'proof · cited by 25
- MeasureTheory.L1.norm_defproof · cited by 4
- MeasureTheory.eLpNorm_le_eLpNorm_mul_rpow_measure_univproof · cited by 3
- MeasureTheory.eLpNorm_le_eLpNorm_top_mul_eLpNormproof · cited by 3
- MeasureTheory.eLpNorm_smul_measure_of_ne_zeroproof · cited by 3
- MeasureTheory.L1.norm_eq_integral_normproof · cited by 3
- MeasureTheory.eLpNorm'_le_eLpNormEssSup_mul_rpow_measure_univstatement and proof · cited by 3
- MeasureTheory.ae_le_eLpNormEssSupstatement · cited by 3
- MeasureTheory.eLpNormEssSup_conststatement · cited by 3