Theorems · Definition · measure theory
MeasureTheory.Measure.toFinite
{α : Type u_1} →
{mα : MeasurableSpace α} → (μ : MeasureTheory.Measure α) → [MeasureTheory.SFinite μ] → MeasureTheory.Measure αA finite measure obtained from an s-finite measure μ, such that
μ = μ.toFinite.withDensity (μ.rnDeriv μ.toFinite)
(see MeasureTheory.Measure.withDensity_rnDeriv_eq along with
MeasureTheory.absolutelyContinuous_toFinite). If μ is non-zero, then μ.toFinite is a
probability measure.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasureTheory.SFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Set.univproof · cited by 3,945
- MeasureTheory.SFinitestatement and proof · cited by 449
- ProbabilityTheory.condproof · cited by 43
- MeasureTheory.Measure.toFiniteAuxproof · cited by 4
Cited by10
Results whose statement or proof uses this declaration.
- MeasureTheory.ae_toFinitestatement and proof · cited by 3
- MeasureTheory.absolutelyContinuous_toFinitestatement · cited by 2
- MeasureTheory.toFinite_absolutelyContinuousstatement · cited by 1
- MeasureTheory.sfiniteSeq_absolutelyContinuous_toFinitestatement · cited by 0
- MeasureTheory.Measure.toFinite.congr_simpstatement and proof · cited by 0
- MeasureTheory.restrict_compl_sigmaFiniteSetstatement and proof · cited by 0
- MeasureTheory.toFinite_apply_eq_zero_iffstatement · cited by 0
- MeasureTheory.toFinite_eq_selfstatement · cited by 0
- MeasureTheory.toFinite_eq_zero_iffstatement · cited by 0
- MeasureTheory.toFinite_zerostatement · cited by 0