Theorems · Theorem · real analysis
ENNReal.ofReal_limsup_toReal
∀ {α : Type u_1} {f : Filter α} [f.NeBot] {u : α → ENNReal} {C : NNReal},
(∀ᶠ (a : α) in f, u a ≤ ↑C) → ENNReal.ofReal (Filter.limsup (fun a => (u a).toReal) f) = Filter.limsup u f- Defined in
- Mathlib.Order.Filter.ENNReal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 129 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Filter.NeBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- ENNRealstatement and proof · cited by 9,879
- Filterstatement and proof · cited by 8,121
- NNRealstatement and proof · cited by 4,310
- Filter.Eventuallystatement and proof · cited by 3,134
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- ENNReal.ofRealstatement · cited by 863
- ENNReal.toRealstatement and proof · cited by 859
- Filter.NeBotstatement and proof · cited by 853
- Filter.IsBoundedUnderproof · cited by 247
Cited by1
Results whose statement or proof uses this declaration.