Theorems · Theorem · measure theory

MeasureTheory.exp_llr_of_ac

∀ {α : Type u_1} {mα : MeasurableSpace α} (μ ν : MeasureTheory.Measure α) [MeasureTheory.SigmaFinite μ]
  [μ.HaveLebesgueDecomposition ν],
  μ.AbsolutelyContinuous ν → (fun x => Real.exp (MeasureTheory.llr μ ν x)) =ᵐ[μ] fun x => (μ.rnDeriv ν x).toReal

Defined in: Mathlib.MeasureTheory.Measure.LogLikelihoodRatio
Cited by: 1 results in Mathlib
Foundations: Depth 216 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasureTheory.SigmaFinite MeasureTheory.Measure.HaveLebesgueDecomposition

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Cites19

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

Realstatement and proof · cited by 25,697
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
Set.ofPredproof · cited by 6,101
MeasureTheory.aestatement · cited by 2,352
Filter.EventuallyEqstatement · cited by 1,912
Filter.univ_mem'proof · cited by 1,672
Filter.mp_memproof · cited by 1,537
LT.lt.ne'proof · cited by 1,417
Real.expstatement and proof · cited by 871
ENNReal.toRealstatement and proof · cited by 859
MeasureTheory.SigmaFinitestatement and proof · cited by 526

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.exp_neg_llr'proof · cited by 0