Theorems · Theorem · order theory
Filter.limsup_le_iSup
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] {f : Filter β} {u : β → α}, Filter.limsup u f ≤ ⨆ n, u n- Defined in
- Mathlib.Order.LiminfLimsup
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- iSupstatement · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- Filter.Eventually.of_forallproof · cited by 526
- Filter.limsupstatement · cited by 226
- le_iSupproof · cited by 207
- Filter.isCobounded_le_of_botproof · cited by 58
- Filter.limsup_le_of_leproof · cited by 11
Cited by7
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.indep_limsup_selfproof · cited by 5
- ProbabilityTheory.Kernel.indep_iSup_directed_limsupproof · cited by 3
- ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup_atBotproof · cited by 0
- ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup_atTopproof · cited by 0
- MeasureTheory.isTightMeasureSet_range_iff_tendsto_limsup_innerproof · cited by 0
- MeasureTheory.isTightMeasureSet_range_iff_tendsto_limsup_measure_norm_gtproof · cited by 0
- ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsupproof · cited by 0