Theorems · Theorem · general topology
Filter.EventuallyLE.trans
∀ {α : Type u} {β : Type v} [inst : Preorder β] {l : Filter α} {f g h : α → β}, f ≤ᶠ[l] g → g ≤ᶠ[l] h → f ≤ᶠ[l] h- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Preorderstatement and proof · cited by 7,952
- le_transproof · cited by 985
- Filter.Eventually.monoproof · cited by 646
- Filter.EventuallyLEstatement and proof · cited by 383
- Filter.Eventually.mpproof · cited by 78
Cited by27
Results whose statement or proof uses this declaration.
- MeasureTheory.integral_mono_of_nonnegproof · cited by 16
- Filter.limsup_le_limsupproof · cited by 16
- Filter.EventuallyLE.trans_eqproof · cited by 8
- MeasureTheory.Submartingale.negproof · cited by 7
- Filter.EventuallyEq.trans_leproof · cited by 4
- limsup_eq_botproof · cited by 3
- MeasureTheory.hasSum_setToFun_of_dominated_convergenceproof · cited by 3
- MeasureTheory.Supermartingale.negproof · cited by 3
- MeasureTheory.Submartingale.condExp_sub_nonnegproof · cited by 3
- MeasureTheory.ae_bdd_norm_condExp_of_ae_bdd_normproof · cited by 2
- interior_ae_eq_of_null_frontierproof · cited by 2
- MeasureTheory.submartingale_of_condExp_sub_nonneg_natproof · cited by 2