Three problems from the theory of right processes (Q1091042)

The author studies some properties of so called right processes in a non- Borel setup. It is shown that there exists a probability measure \(P^ x_ Z\) on the space of continuous functions from [0,\(\infty)\) into \({\mathbb{R}}^ n\) \((f(0)=x)\) with Z being a universally measurable null set in \({\mathbb{R}}^ n\) such that \((X_ t,P^ x_ Z)\) has not realization as a right process, where \(X_ t\) stands for the coordinate process. At the same time one constructs \((X_ t,P^ x_ Z)\) that enjoys both realizations.