Theorems · Theorem · measure theory

essInf_eq_ciInf

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  [inst : ConditionallyCompleteLattice β] {f : α → β} [Nonempty α],
  (∀ (a : α), μ {a} ≠ 0) → BddBelow (Set.range f) → essInf f μ = ⨅ a, f a

Defined in

Mathlib.MeasureTheory.Function.EssSup

Cited by

2 results in Mathlib

Foundations

Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ConditionallyCompleteLatticeNonempty