Theorems · Theorem · measure theory
MeasureTheory.Measure.FiniteSpanningSetsIn.ext
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ ν : MeasureTheory.Measure α} {C : Set (Set α)},
m0 = MeasurableSpace.generateFrom C → IsPiSystem C → ∀ (h : μ.FiniteSpanningSetsIn C), (∀ s ∈ C, μ s = ν s) → μ = νAn extensionality for measures. It is ext_of_generateFrom_of_iUnion formulated in terms of
FiniteSpanningSetsIn.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- LT.lt.neproof · cited by 872
- MeasurableSpace.generateFromstatement and proof · cited by 172
- IsPiSystemstatement and proof · cited by 88
- MeasureTheory.Measure.FiniteSpanningSetsInstatement and proof · cited by 23
- MeasureTheory.Measure.FiniteSpanningSetsIn.setproof · cited by 10
- MeasureTheory.Measure.FiniteSpanningSetsIn.set_memproof · cited by 7
- MeasureTheory.Measure.FiniteSpanningSetsIn.spanningproof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.prod_eq_generateFromproof · cited by 3
- MeasureTheory.Measure.pi_eq_generateFromproof · cited by 2
- Real.measure_ext_Ioo_ratproof · cited by 2
- MeasureTheory.measurePreserving_arrowProdEquivProdArrowproof · cited by 1