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Theorems · Theorem · general topology

EReal.le_limsup_add

∀ {α : Type u_3} {f : Filter α} {u v : α → EReal}, Filter.limsup u f + Filter.liminf v f ≤ Filter.limsup (u + v) f
Defined in
Mathlib.Topology.Instances.EReal.Lemmas
Cited by
2 results in Mathlib
Foundations
Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

LinearGrowth.le_linearGrowthSup_add · cited by 1LinearGrowth.le_linearGro…ExpGrowth.le_expGrowthSup_mul · cited by 1ExpGrowth.le_expGrowthSup…Filter · cited by 8121FilterEReal · cited by 793ERealLT.lt.trans · cited by 370lt.transFilter.limsup · cited by 226Filter.limsupFilter.liminf · cited by 198Filter.liminfFilter.isBounded_le_of_top · cited by 75Filter.isBounded_le_of_topFilter.Frequently.mono · cited by 64Frequently.monoFilter.isCobounded_le_of_bot · cited by 58Filter.isCobounded_le_of_…Filter.isBounded_ge_of_bot · cited by 55Filter.isBounded_ge_of_botFilter.Frequently.and_eventually · cited by 49Frequently.and_eventuallyFilter.eventually_lt_of_lt_liminf · cited by 17Filter.eventually_lt_of_l…EReal.add_lt_add · cited by 12EReal.add_lt_addFilter.le_limsup_iff · cited by 10Filter.le_limsup_iffFilter.frequently_lt_of_lt_limsup · cited by 10Filter.frequently_lt_of_l…EReal.add_le_of_forall_lt · cited by 3EReal.add_le_of_forall_ltEReal.le_limsup_addCITED BYCITES

Cites15

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Cited by2

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