Finite Dimensional Approximations to Some Flows on the Projective Limit Space of Spheres
Hisao Nomoto · Nagoya Mathematical Journal · 1966
LetΩbe the projective limit space of a sequence of probability spaceΩnwhich is a certain subset of (n− 1)-dimensional sphere with the usual uniform probability distribution on it. T. Hida [2], starting from a sequence of finite dimensional flows which are derived from some one-parameter subgroups of rotations of spheres, constructed a flow {Tt} onΩas the limit of them. Observing his method, the concept ofconsistencyof flows which approximate {Tt} seems to play an essential role in his work [2]. As will be made clear in the following sections, the concept of consistency is closely related to the projective limiting structure of our basic spaceΩ. The purpose of this paper is to determine all the flows onΩwhich can be approximated in the sense of [2] by finite dimensional flows.