essSup — Mathlib

English

If f maps α to β with finite α and a measurableSingletonClass, then essInf f .count equals the iInf of f(a).

Русский

Если α конечен и есть класс единичных подмножеств, essInf f .count равен iInf f(a).

LaTeX

$$$[Finite α] (hf : BddBelow (Set.range f)) : \operatorname{essInf} f (MeasureTheory.uniformOn univ) = \iInf a, f a$.$$

Lean4

/-- Essential supremum of `f` with respect to measure `μ`: the smallest `c : β` such that
`f x ≤ c` a.e. -/
def essSup {_ : MeasurableSpace α} (f : α → β) (μ : Measure α) :=
  (ae μ).limsup f

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