Effective dimension of points visited by Brownian motion

(with Anil Nerode). Theoretical Computer Science **410** (2009), no. 4-5, 347—354.

Preliminary version: The law of the iterated logarithm for algorithmically random paths of Brownian motion.

Logical Foundations of Computer Science, *Lecture Notes in Computer Science,* vol. 4514, Springer, Berlin, 2007, pp. 310—317.

In this paper we answered a question of Fouché regarding algorithmically random Brownian motion. The key idea was to use Carathéodory’s measure algebra isomorphism theorem.