Theorems · Theorem · functional analysis
MeasureTheory.eLpNormEssSup_le_of_ae_bound
∀ {α : Type u_1} {F : Type u_5} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup F]
{f : α → F} {C : ℝ}, (∀ᵐ (x : α) ∂μ, ‖f x‖ ≤ C) → MeasureTheory.eLpNormEssSup f μ ≤ ENNReal.ofReal C- Cited by
- 3 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Norm.normstatement and proof · cited by 5,413
- LE.le.transproof · cited by 3,151
- Filter.Eventuallystatement and proof · cited by 3,134
- MeasureTheory.aestatement and proof · cited by 2,352
- ENNReal.ofRealstatement · cited by 863
- Filter.Eventually.monoproof · cited by 646
- MeasureTheory.eLpNormEssSupstatement · cited by 59
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.eLpNormEssSup_lt_top_of_ae_boundproof · cited by 3
- SchwartzMap.norm_toLp_top_leproof · cited by 1
- HasCompactSupport.exist_eLpNorm_sub_le_of_continuousproof · cited by 1