THE PSEUDO PROBABILITY

Ljubo M. Nedović – Tatjana Grbić

   Let (I,⊕,⊙) be a semiring with a neutral element 0 of the ⊕ and a neutral element 1 of the ⊙. Let Σ be a σ-algebra of subsets of a nonempty set Ω. Pseudo probability is a function P: Σ→ I with the next properties: (1) P(∅) = 0 and P(Ω) = 1, (2) P(∪_i=1^∞ A_i) = ⊕_i=1^∞ P(A_i) for pairwise disjoint sets {A_i}_{i ∈ N} from Σ. The triple (Ω,Σ,P) is called a pseudo probability space. In this paper some properties of the pseudo probability space and the pseudo variables are presented.

Keywords: semiring, pseudo-operation, pseudo-probability, pseudo-variable, law of large numbers

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