Theorems · Theorem · measure theory

MeasureTheory.integrable_llr_tilted_left

∀ {α : Type u_1} {mα : MeasurableSpace α} {μ ν : MeasureTheory.Measure α} {f : α → ℝ} [MeasureTheory.IsFiniteMeasure μ]
  [MeasureTheory.SigmaFinite ν],
  μ.AbsolutelyContinuous ν →
    MeasureTheory.Integrable f μ →
      MeasureTheory.Integrable (MeasureTheory.llr μ ν) μ →
        MeasureTheory.Integrable (fun x => Real.exp (f x)) μ →
          AEMeasurable f ν → MeasureTheory.Integrable (MeasureTheory.llr (μ.tilted f) ν) μ

Defined in: Mathlib.MeasureTheory.Measure.LogLikelihoodRatio
Cited by: 0 results in Mathlib
Foundations: Depth 259 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasureTheory.IsFiniteMeasure MeasureTheory.SigmaFinite

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Cites18

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
MeasureTheory.integralproof · cited by 1,779
MeasureTheory.Integrablestatement and proof · cited by 1,367
MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
Real.logproof · cited by 939
Real.expstatement and proof · cited by 871
AEMeasurablestatement and proof · cited by 840
MeasureTheory.SigmaFinitestatement and proof · cited by 526
MeasureTheory.Measure.AbsolutelyContinuousstatement and proof · cited by 325
MeasureTheory.integrable_constproof · cited by 73

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