essInf — Mathlib

English

When α is finite and μ is uniform, essInf equals infimum over a of f(a).

Русский

При конечной α и униформной мере essInf равен инф-пределу по a: f(a).

LaTeX

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

Lean4

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

Похожие утверждения