biInf — Mathlib

English

If s is a set and f_i are AEMeasurable, then the a.e. measurable supremum over i∈s is AEMeasurable.

Русский

Если f_i — AEMеас measurable, то на множесто s верхняя граница по i — AEMеас measurable.

LaTeX

$$theorem AEMeasurable.biSup {ι} {μ : Measure δ} (s : Set ι) {f : ι → δ → α} (hs : s.Countable) (hf : ∀ i ∈ s, AEMeasurable (f i) μ) : AEMeasurable (fun b => ⨆ i ∈ s, f i b) μ$$

Lean4

theorem biInf {ι} {μ : Measure δ} (s : Set ι) {f : ι → δ → α} (hs : s.Countable) (hf : ∀ i ∈ s, AEMeasurable (f i) μ) :
    AEMeasurable (fun b => ⨅ i ∈ s, f i b) μ :=
  .biSup (α := αᵒᵈ) s hs hf

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