Theorems · Theorem · information theory
InformationTheory.leftDeriv_klFun
∀ {x : ℝ}, derivWithin InformationTheory.klFun (Set.Iio x) x = Real.log xThe left derivative of klFun is log x. This also holds at x = 0 although klFun is not
differentiable there since the default value of derivWithin in that case is 0.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Set.Iiostatement and proof · cited by 1,166
- Real.logstatement and proof · cited by 939
- derivWithinstatement and proof · cited by 258
- HasDerivAt.hasDerivWithinAtproof · cited by 86
- Real.log_zeroproof · cited by 84
- HasDerivWithinAt.derivWithinproof · cited by 62
- InformationTheory.klFunstatement and proof · cited by 36
- derivWithin_zero_of_not_differentiableWithinAtproof · cited by 12
- uniqueDiffWithinAt_Iioproof · cited by 4
- InformationTheory.hasDerivAt_klFunproof · cited by 3
- InformationTheory.not_differentiableWithinAt_klFun_Iio_zeroproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- InformationTheory.leftDeriv_klFun_oneproof · cited by 0