Theorems · Definition · measure theory

MeasureTheory.Measure.FiniteSpanningSetsIn.disjointed

{α : Type u_1} →
  {m0 : MeasurableSpace α} →
    {μ : MeasureTheory.Measure α} →
      μ.FiniteSpanningSetsIn {s | MeasurableSet s} → μ.FiniteSpanningSetsIn {s | MeasurableSet s}

Given S : μ.FiniteSpanningSetsIn {s | MeasurableSet s}, FiniteSpanningSetsIn.disjointed provides a FiniteSpanningSetsIn {s | MeasurableSet s} such that its underlying sets are pairwise disjoint.

Defined in: Mathlib.MeasureTheory.Measure.Typeclasses.SFinite
Cited by: 2 results in Mathlib
Foundations: Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement and proof · cited by 53,352
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
Set.ofPredstatement and proof · cited by 6,101
MeasurableSetstatement and proof · cited by 3,075
disjointedproof · cited by 64
MeasureTheory.Measure.FiniteSpanningSetsInstatement and proof · cited by 23
MeasureTheory.Measure.FiniteSpanningSetsIn.setproof · cited by 10

Cited by2

Results whose statement or proof uses this declaration.

MeasureTheory.Measure.FiniteSpanningSetsIn.disjointed_set_eqstatement · cited by 0
MeasureTheory.Measure.exists_eq_disjoint_finiteSpanningSetsInproof · cited by 0