Theorems · Theorem · measure theory
VitaliFamily.eventually_filterAt_subset_of_nhds
∀ {X : Type u_1} [inst : PseudoMetricSpace X] {m0 : MeasurableSpace X} {μ : MeasureTheory.Measure X}
(v : VitaliFamily μ) {x : X} {o : Set X}, o ∈ nhds x → ∀ᶠ (t : Set X) in v.filterAt x, t ⊆ o- Cited by
- 4 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Filter.Eventuallystatement · cited by 3,134
- PseudoMetricSpacestatement and proof · cited by 1,550
- inf_le_leftproof · cited by 286
- Filter.Eventually.filter_monoproof · cited by 84
- VitaliFamilystatement and proof · cited by 68
- VitaliFamily.filterAtstatement · cited by 49
- Filter.eventually_smallSets_subsetproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- VitaliFamily.measure_le_of_frequently_leproof · cited by 5
- VitaliFamily.eventually_filterAt_integrableOnproof · cited by 2
- VitaliFamily.ae_tendsto_lintegral_enorm_sub_divproof · cited by 1
- VitaliFamily.ae_tendsto_lintegral_enorm_sub_div'_of_integrableproof · cited by 1