The upshot of the paper is that one can have, for virtually all familiar, "continuous" spaces, a representation in terms of a discrete finitely additive space in which measurability is not an issue. The qualifier "virtually" above refers to the fact that any complete separable metric space can be embedded as a subset of the product space {0,1}^N of infinite coin flips. The finitely additive space constructed is "discrete" in the sense that every subset is measurable.

The paper's results are (or can be) used to model a host of phenomena of interest to economists: purification and the law of large numbers in large games, complexity, learning, all are issues taken up by various papers of mine.

SLIDES:

Slides cover both this paper and "large games and the law of large numbers "