PLANES AND CONVEXITY. I'm substitute teaching a graduate level game theory class this semester, and I'm seeking clarification of a few subtleties. It appears to me that there are some fundamental theorems establishing equivalences among minimax solutions of various kinds, saddle points, and separating hyperplanes. I can manage that. Now comes the Borel algebras and the Borel probability measures. These appear to be tools to contemplate mixed strategies on continuous strategy spaces, i.e. in games where a player competes in quantities or in prices, and each quantity or price is a set of measure zero. I'm probably missing something in that interpretation: clarifications or sources of clarification are welcome.