Theorems · Theorem · measure theory
MeasureTheory.mem_spanningSetsIndex
∀ {α : Type u_1} {m0 : MeasurableSpace α} (μ : MeasureTheory.Measure α) [inst : MeasureTheory.SigmaFinite μ] (x : α),
x ∈ MeasureTheory.spanningSets μ (MeasureTheory.spanningSetsIndex μ x)- Cited by
- 6 results in Mathlib
- Foundations
- Depth 189 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.SigmaFinitestatement and proof · cited by 526
- MeasureTheory.spanningSetsstatement and proof · cited by 45
- disjointed_subsetproof · cited by 14
- MeasureTheory.spanningSetsIndexstatement and proof · cited by 14
- MeasureTheory.mem_disjointed_spanningSetsIndexproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.rnDeriv_lt_topproof · cited by 21
- MeasureTheory.ae_of_forall_measure_lt_top_ae_restrict'proof · cited by 3
- MeasureTheory.measure_singleton_lt_topproof · cited by 2
- MeasureTheory.mem_spanningSets_of_index_leproof · cited by 1
- VitaliFamily.exists_measurable_supersets_limRatioproof · cited by 1
- MeasureTheory.summable_norm_of_tsum_eLpNorm_ne_topproof · cited by 0