Theorems · Theorem · measure theory
MeasureTheory.iUnion_spanningSets
∀ {α : Type u_1} {m0 : MeasurableSpace α} (μ : MeasureTheory.Measure α) [inst : MeasureTheory.SigmaFinite μ],
⋃ i, MeasureTheory.spanningSets μ i = Set.univ- Cited by
- 19 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.
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.univstatement and proof · cited by 3,945
- Set.iUnionstatement · cited by 2,483
- MeasureTheory.SigmaFinitestatement and proof · cited by 526
- MeasureTheory.spanningSetsstatement · cited by 45
- MeasureTheory.Measure.toFiniteSpanningSetsInproof · cited by 13
- MeasureTheory.Measure.FiniteSpanningSetsIn.spanningproof · cited by 7
- Set.iUnion_accumulateproof · cited by 7
Cited by19
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.add_right_injproof · cited by 7
- MeasureTheory.isCountablySpanning_spanningSetsproof · cited by 4
- MeasureTheory.sigmaFiniteTrim_monoproof · cited by 4
- MeasureTheory.SigmaFinite.of_mapproof · 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.lintegral_abs_det_fderiv_le_addHaar_imageproof · cited by 1
- MeasureTheory.Measure.iSup_restrict_spanningSets_of_measurableSetproof · cited by 1
- MeasureTheory.setIntegral_condExpL1CLMproof · cited by 1
- MeasureTheory.sigmaFinite_bot_iffproof · cited by 1