Giving a sequence \(P=(P_{n})_{n}\) of kernels on a measurable space (or just a semigroup \((P_{t})_{t\in (0,\infty )}\) ), we are interested to describe the “semi-excessive” functions w.r. to P, i.e., measurable functions f, such that \(\lim \nolimits _{n\rightarrow \infty } P_{n}(f)=f\) (or \(\lim \nolimits _{t\rightarrow 0} P_{t}(f)=f\) ). We extend in this frame the famous Korovkin result on the uniform convergence of \(P_{n}(f)\) to f on a class of measurable functions f, but beside that, we give a pointwise convergence result which may be a useful tool in Probabilistic Potential Theory as well Right Processes.
