Theorems · Theorem · measure theory

meas_lt_essInf

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  [inst : ConditionallyCompleteLinearOrder β] {f : α → β} [inst_1 : TopologicalSpace β] [FirstCountableTopology β]
  [OrderTopology β],
  autoParam (Filter.IsBoundedUnder (fun x1 x2 => x1 ≥ x2) (MeasureTheory.ae μ) f) meas_lt_essInf._auto_1 →
    μ {y | f y < essInf f μ} = 0

Defined in

Mathlib.MeasureTheory.Function.EssSup

Cited by

0 results in Mathlib

Foundations

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

Assumes

ConditionallyCompleteLinearOrderTopologicalSpaceFirstCountableTopologyOrderTopology