Theorems · Theorem · measure theory

MeasureTheory.llr_smul_nnreal_right

∀ {α : Type u_1} {mα : MeasurableSpace α} {μ ν : MeasureTheory.Measure α} [MeasureTheory.IsFiniteMeasure μ]
  [μ.HaveLebesgueDecomposition ν],
  μ.AbsolutelyContinuous ν →
    ∀ (c : NNReal), c ≠ 0 → MeasureTheory.llr μ (c • ν) =ᵐ[μ] fun x => MeasureTheory.llr μ ν x - Real.log ↑c

Defined in: Mathlib.MeasureTheory.Measure.LogLikelihoodRatio
Cited by: 2 results in Mathlib
Foundations: Depth 217 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasureTheory.IsFiniteMeasure 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
ENNRealstatement · cited by 9,879
NNRealstatement and proof · cited by 4,310
MeasureTheory.aestatement and proof · cited by 2,352
Filter.EventuallyEqstatement and proof · cited by 1,912
Filter.univ_mem'proof · cited by 1,672
Filter.mp_memproof · cited by 1,537
ENNReal.ofNNRealproof · cited by 1,279
NNReal.toRealstatement and proof · cited by 1,260
MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078

Cited by2

Results whose statement or proof uses this declaration.

InformationTheory.toReal_klDiv_smul_right_eq_smul_leftproof · cited by 3
InformationTheory.klDiv_smul_right_eq_smul_leftproof · cited by 0