Theorems · Theorem · information theory
Real.qaryEntropy_continuous
∀ {q : ℕ}, Continuous (Real.qaryEntropy q)The q-ary entropy function is continuous everywhere.
This is due to definition of Real.log for negative numbers.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 213 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Continuousstatement · cited by 2,592
- Real.logproof · cited by 939
- continuous_id'proof · cited by 295
- Continuous.comp'proof · cited by 184
- Continuous.prodMkproof · cited by 127
- continuous_addproof · cited by 47
- Real.qaryEntropystatement · cited by 18
- Continuous.mul_constproof · cited by 15
- Real.binEntropy_continuousproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Real.strictConcaveOn_qaryEntropyproof · cited by 1
- Real.qaryEntropy_strictAntiOnproof · cited by 1
- Real.qaryEntropy_strictMonoOnproof · cited by 1