  Brownian motions in the infinite-dimensional group of all unitary operators
are studied under strong continuity assumption rather than norm continuity.
Every such motion can be described in terms of a countable collection of
independent one-dimensional Brownian motions. The proof involves continuous
tensor products and continuous quantum measurements. A by-product: a Brownian
motion in a separable F-space (not locally convex) is a Gaussian process.
