via
thisbirdcansing Open the nearest book to page 56.
Write out the fifth sentence on that page, and also the next two to five sentences.
The CLOSEST BOOK, NOT YOUR FAVORITE, OR MOST INTELLECTUAL!
"The line segment joining p* to p' is the set of points (1-a)p* + ap', 0 =< a =< 1. Note that the line segment lies entirely within S. If we examine the values of g along this segment we find by convexity that
{g[(1-a)p* + ap'] - g(p*)}/{a} >= {(1-a)g(p*) +ag(p') - g(p*)}/{a} = g(p') - g(p*) > 0 ,
as long as 0 < a =< 1. "
Robert B. Ash, Information Theory
... It's not even any of the cool stuff.