Theorems · Theorem · measure theory
ENNReal.essSup_restrict_eq_of_support_subset
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α} {f : α → ENNReal},
Function.support f ⊆ s → essSup f (μ.restrict s) = essSup f μ- Defined in
- Mathlib.MeasureTheory.Function.EssSup
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites33
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Set.ofPredproof · cited by 6,101
- le_antisymmproof · cited by 2,068
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- le_rflproof · cited by 1,558
- LT.lt.ne'proof · cited by 1,417
- LT.lt.trans_leproof · cited by 678
- ne_of_gtproof · cited by 637
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.eLpNorm_restrict_eq_of_support_subsetproof · cited by 1