Základy theorie integrálu v Euklidových prostorech. [I.]
We prove that the notions of Krengel entropy and Poisson entropy for infinite-measure-preserving transformations do not always coincide: We construct a conservative infinite-measure-preserving transformation with zero Krengel entropy (the induced transformation on a set of measure 1 is the Von Neumann–Kakutani odometer), but whose associated Poisson suspension has positive entropy.
Suppose is a finite positive rotation invariant Borel measure on the open unit disc , and that the unit circle lies in the closed support of . For the Bergman space is the collection of functions in holomorphic on . We show that whenever a Gaussian power series almost surely lies in but not in , then almost surely: a) the zero set of is not contained in any zero set (, and b) is not contained in any zero set.