In a problem I'm working on I found myself with a point $y\in \mathbb{R}^m$ lying at the boundary of a non-closed convex set $K$. I'd like to express it as as "infinite convex combination" $y=\sum_{i=1}^\infty \lambda_i y_i,$ where $\lambda_i \ge 0$, $\sum_i \lambda_i=1$ and $y_i \in K$ for all indices $i$. May I do so?
Thank you.