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A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.
3
votes
Brownian motion and spheres
H.P. McKean wrote a fun paper on this topic. He argues that one can think of Wiener measure as uniform measure on an infinite-dimensional sphere with radius "$\sqrt{\infty}$".
See http://www.jstor.or …