Theorems · Definition · measure theory
essInf
{α : Type u_1} →
{β : Type u_2} → [ConditionallyCompleteLattice β] → {x : MeasurableSpace α} → (α → β) → MeasureTheory.Measure α → βEssential infimum of f with respect to measure μ: the greatest c : β such that
c ≤ f x a.e.
- Defined in
- Mathlib.MeasureTheory.Function.EssSup
- Cited by
- 18 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.liminfproof · cited by 198
Cited by18
Results whose statement or proof uses this declaration.
- essInf_eq_ciInfstatement · cited by 2
- ae_essInf_lestatement · cited by 1
- essInf_const'statement · cited by 1
- essInf_eq_iInfstatement · cited by 1
- le_essInf_of_ae_lestatement · cited by 0
- ae_lt_of_lt_essInfstatement and proof · cited by 0
- essInf_antitone_measurestatement · cited by 0
- essInf_cond_count_eq_ciInfstatement · cited by 0
- essInf_congr_aestatement · cited by 0
- essInf_conststatement · cited by 0
- essInf_const_topstatement · cited by 0
- essInf_countstatement · cited by 0