Theorems · Theorem · information theory
InformationTheory.klDiv_self
∀ {α : Type u_1} {mα : MeasurableSpace α} (μ : MeasureTheory.Measure α) [MeasureTheory.SigmaFinite μ],
InformationTheory.klDiv μ μ = 0- Cited by
- 4 results in Mathlib
- Foundations
- Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasureTheory.SigmaFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · 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
- Set.univproof · cited by 3,945
- zero_addproof · cited by 2,366
- MeasureTheory.aeproof · cited by 2,352
- Filter.EventuallyEqproof · cited by 1,912
- sub_selfproof · cited by 996
- ENNReal.ofRealproof · cited by 863
- MeasureTheory.Measure.realproof · cited by 530
- MeasureTheory.SigmaFinitestatement and proof · cited by 526
Cited by4
Results whose statement or proof uses this declaration.
- InformationTheory.toReal_klDiv_smul_right_eq_smul_leftproof · cited by 3
- InformationTheory.toReal_klDiv_smul_sameproof · cited by 1
- InformationTheory.klDiv_eq_zero_iffproof · cited by 0
- InformationTheory.klDiv_smul_sameproof · cited by 0