Theorems · Theorem · measure theory
MeasureTheory.measure_spanningSets_lt_top
∀ {α : Type u_1} {m0 : MeasurableSpace α} (μ : MeasureTheory.Measure α) [inst : MeasureTheory.SigmaFinite μ] (i : ℕ),
μ (MeasureTheory.spanningSets μ i) < ⊤- Cited by
- 25 results in Mathlib
- Foundations
- Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasureTheory.SigmaFinite
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.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Top.topstatement · cited by 9,680
- MeasureTheory.SigmaFinitestatement and proof · cited by 526
- MeasureTheory.spanningSetsstatement · cited by 45
- Set.finite_le_natproof · cited by 16
- MeasureTheory.Measure.toFiniteSpanningSetsInproof · cited by 13
- MeasureTheory.measure_biUnion_lt_topproof · cited by 8
- MeasureTheory.Measure.FiniteSpanningSetsIn.finiteproof · cited by 5
Cited by25
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.rnDeriv_lt_topproof · cited by 21
- MeasureTheory.Measure.add_right_injproof · cited by 7
- ConvexOn.map_condExp_leproof · cited by 4
- MeasureTheory.ae_eq_zero_of_forall_setIntegral_eq_of_sigmaFiniteproof · cited by 3
- MeasurableEmbedding.sigmaFinite_mapproof · cited by 3
- MeasureTheory.sigmaFinite_restrict_sigmaFiniteSetWRT'proof · cited by 3
- MeasureTheory.ae_of_forall_measure_lt_top_ae_restrict'proof · cited by 3
- MeasureTheory.ae_le_of_forall_setLIntegral_le_of_sigmaFinite₀proof · cited by 2
- MeasureTheory.measure_singleton_lt_topproof · cited by 2
- MeasureTheory.Measure.exists_subset_measure_lt_topproof · cited by 2
- MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_imageproof · cited by 1