Theorems · Theorem · measure theory
essInf_count_eq_ciInf
∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} [inst : ConditionallyCompleteLattice β] {f : α → β} [Nonempty α]
[MeasurableSingletonClass α], BddBelow (Set.range f) → essInf f MeasureTheory.Measure.count = ⨅ a, f a- Defined in
- Mathlib.MeasureTheory.Function.EssSup
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- Set.rangestatement and proof · cited by 4,705
- iInfstatement · cited by 1,690
- BddBelowstatement and proof · cited by 401
- ConditionallyCompleteLatticestatement and proof · cited by 364
- MeasurableSingletonClassstatement and proof · cited by 230
- MeasureTheory.Measure.countstatement · cited by 60
- essInfstatement · cited by 18
- MeasureTheory.Measure.count_singleton'proof · cited by 10
- essInf_eq_ciInfproof · cited by 2
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