Theorems · Theorem · measure theory
MeasureTheory.spanningSetsIndex_eq_iff
∀ {α : Type u_1} {m0 : MeasurableSpace α} (μ : MeasureTheory.Measure α) [inst : MeasureTheory.SigmaFinite μ] {x : α}
{n : ℕ}, MeasureTheory.spanningSetsIndex μ x = n ↔ x ∈ disjointed (MeasureTheory.spanningSets μ) n- Cited by
- 1 results in Mathlib
- Foundations
- Depth 187 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.
Cites10
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
- Set.preimageproof · cited by 4,946
- MeasureTheory.SigmaFinitestatement and proof · cited by 526
- Set.ext_iffproof · cited by 90
- disjointedstatement and proof · cited by 64
- MeasureTheory.spanningSetsstatement and proof · cited by 45
- MeasureTheory.spanningSetsIndexstatement and proof · cited by 14
- MeasureTheory.preimage_spanningSetsIndex_singletonproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.mem_disjointed_spanningSetsIndexproof · cited by 1