Theorems · Theorem · real analysis
ENNReal.limsup_const_mul
∀ {α : Type u_1} {f : Filter α} [CountableInterFilter f] {u : α → ENNReal} {a : ENNReal},
Filter.limsup (fun x => a * u x) f = a * Filter.limsup u f- Defined in
- Mathlib.Order.Filter.ENNReal
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CountableInterFilter
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement and proof · cited by 9,879
- Top.topproof · cited by 9,680
- Filterstatement and proof · cited by 8,121
- MulZeroClass.mul_zeroproof · cited by 2,091
- Filter.EventuallyEqproof · cited by 1,912
- Filter.Eventually.monoproof · cited by 646
- Filter.Frequentlyproof · cited by 414
- eq_top_iffproof · cited by 236
- Filter.limsupstatement and proof · cited by 226
- bot_eq_zero'proof · cited by 92
- CountableInterFilterstatement and proof · cited by 78
- Filter.isBounded_le_of_topproof · cited by 75
Cited by3
Results whose statement or proof uses this declaration.
- ENNReal.essSup_const_mulproof · cited by 4
- ENNReal.limsup_mul_leproof · cited by 1
- ENNReal.limsup_mul_constproof · cited by 0