Theorems · Theorem · information theory
Real.binEntropy_continuous
Continuous Real.binEntropy
Binary entropy is continuous everywhere.
This is due to definition of Real.log for negative numbers.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Continuousstatement and proof · cited by 2,592
- continuous_id'proof · cited by 295
- continuous_constproof · cited by 278
- Continuous.comp'proof · cited by 184
- Continuous.prodMkproof · cited by 127
- Continuous.fun_subproof · cited by 53
- continuous_addproof · cited by 47
- Real.binEntropystatement · cited by 28
- Real.binEntropy_eq_negMulLog_add_negMulLog_one_sub'proof · cited by 2
- Real.continuous_negMulLogproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Real.qaryEntropy_continuousproof · cited by 3