Theorems · Theorem · measure theory

MeasureTheory.llr_smul_left

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

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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Cites26

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 and proof · cited by 9,879
Top.topstatement and proof · cited by 9,680
Set.ofPredproof · cited by 6,101
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
LT.lt.ne'proof · cited by 1,417
MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078

Cited by2

Results whose statement or proof uses this declaration.

MeasureTheory.llr_smul_nnreal_leftproof · cited by 4
MeasureTheory.llr_smul_inv_left_eq_smul_rightproof · cited by 1