Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

An elementary proof of Gleason's theorem

Roger Cookea1, Michael Keanea2 and William Morana3

a1 Department of Philosophy, Delft University of Technology

a2 Department of Mathematics, Delft University of Technology

a3 Department of Mathematics, University of Adelaide


Gleason's theorem characterizes the totally additive measures on the closed sub-spaces of a separable real or complex Hilbert space of dimension greater than two. This paper presents an elementary proof of Gleason's theorem which is accessible to undergraduates having completed a first course in real analysis.

(Received October 03 1984)