On Convex Limit Sets and Brownian Motion

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We prove limsup results for nonnegative functionals of convex sets determined by normalized Brownian paths in Banach spaces. This continues the interesting investigation of D. Khoshnevisan into this area, and relates to some classical unsolved isoperimetric problems for the convex hull of curves in ℝd. Section 4 contains the solution of a problem similar to these classical problems.

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