Theorems · Definition · measure theory
essSup
{α : Type u_1} →
{β : Type u_2} → [ConditionallyCompleteLattice β] → {x : MeasurableSpace α} → (α → β) → MeasureTheory.Measure α → βEssential supremum of f with respect to measure μ: the smallest c : β such that
f x ≤ c a.e.
- Defined in
- Mathlib.MeasureTheory.Function.EssSup
- Cited by
- 69 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ConditionallyCompleteLattice
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.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.aeproof · cited by 2,352
- ConditionallyCompleteLatticestatement and proof · cited by 364
- Filter.limsupproof · cited by 226
Cited by70
Results whose statement or proof uses this declaration.
- MeasureTheory.eLpNormEssSupproof · cited by 59
- MeasureTheory.eLpNorm_negproof · cited by 15
- MeasureTheory.eLpNorm_indicator_eq_eLpNorm_restrictproof · cited by 8
- essSup_mono_aestatement · cited by 7
- essSup_eq_sInfstatement · cited by 5
- ENNReal.essSup_const_mulstatement · cited by 4
- ae_le_essSupstatement · cited by 4
- ae_lt_of_essSup_ltstatement and proof · cited by 4
- essSup_congr_aestatement · cited by 4
- essSup_le_of_ae_lestatement · cited by 4
- essSup_map_measurestatement and proof · cited by 3
- essSup_mono_measure'statement · cited by 3