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 σ-algebra into the (ℝ₀⁺, +, ·), the pseudo-probability space is obtained by substituting (ℝ₀⁺, +, ·) with more general structure (I, ⊕, ⊙) called semiring. Set I is usually some subinterval of [–∞, ∞], while operations ⊕ and ⊙ 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.