proof of criterion for convexity
Suppose is continuous and that, for all ,
Then is convex.
We begin by showing that, for any natural numbers and ,
for some and all . Let be a number less than or equal to . Then either or . In the former case we have
In the other case, we can reverse the roles of and .
|Title||proof of criterion for convexity|
|Date of creation||2013-03-22 17:00:23|
|Last modified on||2013-03-22 17:00:23|
|Last modified by||rspuzio (6075)|