A Proof of a Fixed-Point Theorem of Kakutani.

Joseph W. Kitchen

ResearchPublished 1962

A study of a fixed-point theorem having applications in harmonic analysis and ergodic theory. The Memorandum attempts to 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 raised is the construction of an appropriate integral, and arguments are used that are essentially duplications of familiar arguments in the theory of the elementary Riemann integral

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Kitchen, Joseph W., A Proof of a Fixed-Point Theorem of Kakutani. Santa Monica, CA: RAND Corporation, 1962. https://www.rand.org/pubs/research_memoranda/RM3340.html.
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