Theorems · Theorem · measure theory
essSup_measure_zero
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice β] {m : MeasurableSpace α} {f : α → β}, essSup f 0 = ⊥- Defined in
- Mathlib.MeasureTheory.Function.EssSup
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 · cited by 10,939
- Set.ofPredproof · cited by 6,101
- Bot.botstatement and proof · cited by 4,720
- Filter.Eventuallyproof · cited by 3,134
- CompleteLatticestatement and proof · cited by 1,048
- Filter.mapproof · cited by 819
- le_bot_iffproof · cited by 116
- sInf_leproof · cited by 110
- essSupstatement · cited by 69
- MeasureTheory.ae_zeroproof · cited by 32
- Filter.map_botproof · cited by 16
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.eLpNormEssSup_measure_zeroproof · cited by 3
- essInf_measure_zeroproof · cited by 0