Timeline for Shannon entropy of $p(x)(1-p(x))$ is no less than entropy of $p(x)$

10 events

when toggle format	what		by	license	comment
Jan 16, 2019 at 22:42	vote	accept	sunxd
Jan 12, 2019 at 12:10	answer	added	Fedor Petrov		timeline score: 8
Jan 12, 2019 at 9:43	history	edited	Mark Wildon	CC BY-SA 4.0	Made $p$ discrete.
Jan 12, 2019 at 9:40	comment	added	Mark Wildon		Ah: I see. I somehow misread 'finite support' as 'compact support'. I'm going to edit the question to make it clear that the density is discrete.
Jan 12, 2019 at 9:35	comment	added	Fedor Petrov		I guess that density is a misleading word here: $p(x) $ is a measure of atom $\{x\} $.
Jan 12, 2019 at 8:58	comment	added	Mark Wildon		There is something wrong in the setup: a probability density function may take values more than $1$. And without some continuity assumption on $p$ we could have $p(x) \in \{0,1\}$ for all $x$, so $p(x)(1-p(x)) = 0$ always.
Jan 12, 2019 at 8:57	history	edited	Mark Wildon	CC BY-SA 4.0	Put in LaTeX, corrected spelling mistake, removed thank.
Jan 12, 2019 at 8:40	history	edited	YCor		edited tags
Jan 12, 2019 at 8:40	review	First posts
Jan 12, 2019 at 9:16
Jan 12, 2019 at 8:37	history	asked	sunxd	CC BY-SA 4.0