Theorems · Theorem · information theory
InformationTheory.klDiv_eq_top_iff
∀ {α : Type u_1} {mα : MeasurableSpace α} {μ ν : MeasureTheory.Measure α},
InformationTheory.klDiv μ ν = ⊤ ↔ μ.AbsolutelyContinuous ν → ¬MeasureTheory.Integrable (MeasureTheory.llr μ ν) μ- Cited by
- 0 results in Mathlib
- Foundations
- Depth 256 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- MeasureTheory.Measure.AbsolutelyContinuousstatement and proof · cited by 325
- MeasureTheory.llrstatement and proof · cited by 59
- InformationTheory.klDivstatement and proof · cited by 34
- InformationTheory.klDiv_of_not_acproof · cited by 8
- InformationTheory.klDiv_of_not_integrableproof · cited by 8
- InformationTheory.klDiv_of_ac_of_integrableproof · cited by 4
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