Characterization of distributions having a value at a point in the sense of Robinson (Q451012)

In their main result, the authors give an answer to the question of how Robinson's notion of point value is related to the classical definition of point value in the sense of \textit{S. Łojasiewicz} [Stud. Math. 16, 1--36 (1957; Zbl 0086.09405)]. A distribution has a value at a point in the sense of Robinson if and only if it is a continuous function in a neighborhood of that point. Also, this result improves an earlier result of \textit{P. A. Loeb} [Lect. Notes Math. 369, 153--154 (1974; Zbl 0287.26017)].