Theorems · Theorem · real analysis

ENNReal.toReal_limsup

∀ {α : Type u_1} {f : Filter α} {u : α → ENNReal},
  (∀ᶠ (a : α) in f, u a ≠ ⊤) →
    autoParam (Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) f fun a => (u a).toReal) ENNReal.toReal_limsup._auto_1 →
      (Filter.limsup u f).toReal = Filter.limsup (fun a => (u a).toReal) f

Defined in

Mathlib.Order.Filter.ENNReal

Cited by

1 results in Mathlib

Foundations

Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound