Theorems · Theorem · measure theory
MeasureTheory.preimage_spanningSetsIndex_singleton
∀ {α : Type u_1} {m0 : MeasurableSpace α} (μ : MeasureTheory.Measure α) [inst : MeasureTheory.SigmaFinite μ] (n : ℕ),
MeasureTheory.spanningSetsIndex μ ⁻¹' {n} = disjointed (MeasureTheory.spanningSets μ) n- Cited by
- 2 results in Mathlib
- Foundations
- Depth 186 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.
Cites9
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.preimagestatement · cited by 4,946
- MeasureTheory.SigmaFinitestatement and proof · cited by 526
- disjointedstatement · cited by 64
- MeasureTheory.spanningSetsstatement and proof · cited by 45
- MeasureTheory.spanningSetsIndexstatement · cited by 14
- preimage_find_eq_disjointedproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.spanningSetsIndex_eq_iffproof · cited by 1
- MeasureTheory.exists_pos_lintegral_lt_of_sigmaFiniteproof · cited by 1