Theorems · Definition · information theory
Real.binEntropy
ℝ → ℝ
The [binary entropy function](https://en.wikipedia.org/wiki/Binary_entropy_function)
binEntropy p := - p * log p - (1-p) * log (1 - p)
is the Shannon entropy of a Bernoulli random variable with success probability p.
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by29
Results whose statement or proof uses this declaration.
- Real.qaryEntropyproof · cited by 18
- Real.qaryEntropy_twostatement and proof · cited by 4
- Real.differentiableAt_binEntropystatement · cited by 4
- Real.binEntropy_neg_of_negstatement · cited by 4
- Real.binEntropy_onestatement · cited by 4
- Real.binEntropy_one_substatement · cited by 4
- Real.binEntropy_zerostatement · cited by 4
- Real.binEntropy_nonpos_of_nonposstatement · cited by 3
- Real.binEntropy_posstatement · cited by 3
- Real.binEntropy_eq_negMulLog_add_negMulLog_one_sub'statement · cited by 2
- Real.binEntropy_lt_log_twostatement and proof · cited by 2
- Real.deriv_binEntropystatement · cited by 2