TITLE: Who first defined locally convex topological vector spaces?
QUESTION [12 upvotes]: Who first defined the class of locally convex topological vector spaces?

REPLY [6 votes]: The reference to Kolmogorov is Studia Math, 5 (1934), 29-33. In my opinion, the most reliable source of references to classical papers is the book by Dunford-Schwartz, Linear Operators. They mention also the paper of von Neumann.
Kolmogorov writes about convexity in his note.