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Theorems · Theorem · order theory

Filter.le_limsup_of_frequently_le

∀ {α : Type u_1} {ι : Type u_4} [inst : ConditionallyCompleteLattice α] {f : Filter ι} {u : ι → α} {a : α},
  (∃ᶠ (i : ι) in f, a ≤ u i) →
    autoParam (Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) f u) Filter.le_limsup_of_frequently_le._auto_1 →
      a ≤ Filter.limsup u f
Defined in
Mathlib.Order.LiminfLimsup
Cited by
10 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
ConditionallyCompleteLattice
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Filter.le_limsup_iff · cited by 10Filter.le_limsup_iffProbabilityTheory.Kernel.density_nonneg · cited by 5Kernel.density_nonnegENNReal.limsup_const_mul · cited by 3ENNReal.limsup_const_mulFilter.le_limsup_iff' · cited by 3Filter.le_limsup_iff'isNonarchimedean_smoothingFun · cited by 1isNonarchimedean_smoothin…limsup_mul_le · cited by 1limsup_mul_leENNReal.toReal_limsup · cited by 1ENNReal.toReal_limsuple_limsup_mul · cited by 0le_limsup_mulEReal.le_limsup_mul · cited by 0EReal.le_limsup_mulEReal.limsup_mul_le · cited by 0EReal.limsup_mul_leFilter · cited by 8121FilterLE.le.trans · cited by 3151le.transFilter.Eventually · cited by 3134Filter.EventuallyFilter.Frequently · cited by 414Filter.FrequentlyConditionallyCompleteLattice · cited by 364ConditionallyCompleteLatt…Filter.IsBoundedUnder · cited by 247Filter.IsBoundedUnderFilter.limsup · cited by 226Filter.limsupFilter.Frequently.and_eventually · cited by 49Frequently.and_eventuallyFilter.Frequently.exists · cited by 32Frequently.existsFilter.le_limsup_of_le · cited by 5Filter.le_limsup_of_leFilter.le_limsup_of_frequentl…CITED BYCITES

Cites10

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Cited by10

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