Some properties of pseudo-measures and pseudo-probability

This paper is based on the concept and results from the pseudo-probability theory. Since the classical probability is the mapping from some sigma-algebra into the (R₀ ⁺, +, middot), the pseudo-probability space is obtained by substituting (R₀ ⁺, +, middot) with more general structure (I, oplus, odot) called semiring. Set / is usually some subinterval of [-infin, infin], while operations oplus and odot are generalizations of the classical operations, known as pseudo-addition and pseudo-multiplication, respectively. In this paper some properties of the pseudo-probability measures and corresponding integrals constructed in the given setting are investigated.