Which families of finite-dimensional joint distributions are associated with continuous-path, countably additive, stochastic processes?

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Necessary and sufficient conditions on a family of finite-dimensional distributions for it to be the family of finite-dimensional joint distributions of a countably additive stochastic process with continuous paths have been given by Bartoszynski in 1962. The present paper gives such conditions when the parameter space is any compact metric space and, in particular, any compact manifold.