MPEJ Volume 1, No.4, 35pp Received: August 25, 1995, Revised: November 16, 1995, Accepted: November 22, 1995 Gregory F. Lawler Nonintersecting Planar Brownian Motions ABSTRACT: In this paper we construct a measure on pairs of Brownian motions starting at the same point conditioned so their paths do not intersect. The construction of this measure is a start towards the rigorous understanding of nonintersecting Brownian motions as a conformal field. Let $B^1,B^2$ be independent Brownian motions in $\R^2$ starting at distinct points on the unit circle. Let $T_r^j$ be the first time that the $j$th Brownian motion reaches distance $r$ and let $D_r$ be the event $$ D_r = \{B^1[0,T_{e^r}^1] \cap B^2[0,T_{e^r}^2] = \emptyset \} . $$ We construct the measure by considering the limit of the measure induced by Brownian motions conditioned on the event $D_r$.