Leibniz differential and the St. Petersburg paradox

The report will be explained how strictly to introduce the concept of the infinitesimally small probability, so that, in particular, resolves the St. Petersburg paradox. Will be described infinitesimal structure, more subtle than the measure should have a probability space allowing for the introduction of probability (possibly infinitesimal) for all elementary events. This infinitesimally structure is multiplicative. So, in particular, it have infinite products of finite spaces. And all of this is directly related to the concept of Leibniz differential and Perron-Stilties integral, as described by the author in the paper.