nikete

Proof

Let $\Omega$ be finite, and let $P,Q$ be probability distributions on $\Omega$ with $|P - Q|_1 \leq \frac{1}{2}$. Denote $|P-Q|1$ by $\alpha$. Let $H(P) = -\sum{x\in \Omega}p(x)\log p(x).$ We prove $$ |H(P) - H(Q)| \leq \alpha \log!\left(\frac{|\Omega|}{\alpha}\right). $$

Let $\alpha = |P - Q|_1$.

nikete

license:gpl-3.0

nikete

Keybase proof

I hereby claim:

• I am nikete on github.
• I am nikete (https://keybase.io/nikete) on keybase.
• I have a public key whose fingerprint is 110E EA85 D98A 053C 6373 9B31 F216 78D3 62B6 974D

To claim this, I am signing this object: