Theorems · Theorem · information theory
InformationTheory.convexOn_Ioi_klFun
ConvexOn ℝ (Set.Ioi 0) InformationTheory.klFun
klFun is convex on $(0,∞)$.
This is an often useful consequence of convexOn_klFun, which states convexity on $[0, ∞)$.
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- Foundations
- Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- le_rflproof · cited by 1,558
- Set.Ioistatement · cited by 1,463
- ConvexOnstatement · cited by 232
- InformationTheory.klFunstatement · cited by 36
- convex_Ioiproof · cited by 13
- ConvexOn.subsetproof · cited by 9
- InformationTheory.convexOn_klFunproof · cited by 5
- Set.Ioi_subset_Iciproof · cited by 5
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