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Theorems · Theorem · measure theory

essSup_le_iSup

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : CompleteLattice β]
  {f : α → β}, essSup f μ ≤ ⨆ i, f i
Defined in
Mathlib.MeasureTheory.Function.EssSup
Cited by
1 results in Mathlib
Foundations
Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CompleteLattice
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

iSup_eq_essSup · cited by 0iSup_eq_essSupMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureiSup · cited by 2415iSupCompleteLattice · cited by 1048CompleteLatticele_iSup · cited by 207le_iSupMeasureTheory.ae_of_all · cited by 137MeasureTheory.ae_of_allessSup · cited by 69essSupFilter.isCobounded_le_of_bot · cited by 58Filter.isCobounded_le_of_…essSup_le_of_ae_le · cited by 4essSup_le_of_ae_leessSup_le_iSupCITED BYCITES

Cites9

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Cited by1

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