A PROOF OF A FIXED-POINT THEOREM OF KAKUTANI

The objective of this analysis is t give an elegant and conceptually interesting proof of a fixed-point theorem of Kakutani, and to elucidate the intimate connection between this theorem and the existence of Haar measure on a compact group. The only difficult point in the discussion is the construction of an appropriate integal, and even here the arguments are essentially duplication of familiar arguments in the theory of the elementary Riemann integral. Author