Theorems · Theorem · general topology
ENNReal.liminf_mul_le
∀ {ι : Type u_4} {f : Filter ι} {u v : ι → ENNReal},
Filter.limsup u f ≠ 0 ∨ Filter.liminf v f ≠ ⊤ →
Filter.limsup u f ≠ ⊤ ∨ Filter.liminf v f ≠ 0 → Filter.liminf (u * v) f ≤ Filter.limsup u f * Filter.liminf v f- Cited by
- 0 results in Mathlib
- Foundations
- Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
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.topstatement and proof · cited by 9,680
- Filterstatement and proof · cited by 8,121
- LT.lt.transproof · cited by 370
- Filter.limsupstatement and proof · cited by 226
- Filter.liminfstatement and proof · cited by 198
- Filter.isBounded_le_of_topproof · cited by 75
- Filter.Frequently.monoproof · cited by 64
- Filter.isBounded_ge_of_botproof · cited by 55
- Filter.Frequently.and_eventuallyproof · cited by 49
- Filter.isCobounded_ge_of_topproof · cited by 38
- Filter.eventually_lt_of_limsup_ltproof · cited by 21
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