In this article we give a classi cation of the binary, simple, ω−categorical structures with SU−rank 1 and trivial pregeometry. This is done both by showing that they satisfy certain extension properties, but also by noting that they may be approximated by the almost sure theory of some sets of nite structures equipped with a probability measure. This study give results about general almost sur...

An integral analogue of the general almost sure limit theorem is presented. In the theorem, instead of a sequence of random elements, a continuous time random process is involved, moreover, instead of the logarithmical average, the integral of delta-measures is considered. Then the general theorem is applied to obtain almost sure versions of limit theorems for semistable and max-semistable proc...