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It is shown that, almost surely, for all natural n, there are points which the plane Brownian motion visits exactly n times. [ABSTRACT FROM AUTHOR]

The main result is that in every complete locally-bounded linear topological space there exist series which are unconditionally yet not absolutely convergent. Relations between absolute, unconditional and metric convergence of series are studied. [ABSTRACT FROM AUTHOR]

Paley, Wiener and Zygmund proved that, with probability 1, Brownian paths never satisfy a Lipschitz condition of order greater than 1/2. This result is improved by showing that they never satisfy even a Lipschitz condition of order 1/2 with a sufficiently small Lipschitz constant. [ABSTRACT FROM AUTHOR]