A subset $A$ of a Banach space is called Banach-Saks when every sequence in $A$ has a Ces{`a}ro convergent subsequence. Our interest here focusses on the following problem: is the convex hull of a Banach-Saks set again Banach-Saks? By means of a comb
inatorial argument, we show that in general the answer is negative. However, sufficient conditions are given in order to obtain a positive result.
