ABSTRACT
Mathematics, including Probability Theory, hinges upon bivalent Logics and
its set theoretical derivatives. In Probability Theory one assumes that when per-
forming an experiment with more than one possible outcome, these outcomes
form a set, the sample space, and the probability (chance) of a particular event
(subset of outcomes) to occur, accumulates from probabilities of its disjoint
parts (subevents). A more formal definition is:
DEFINITION 2.1.1. (i) A A is a set of subsets, called events, of a nonempty set Ω , called sample space, defined by the requirements that
Ω ∈A, ∀E ∈ A⇒ Ec ∈A, (2.1)
∀E1,E2, · · · ∈ A⇒∪∞k=1Ek ∈ A. (ii) A measure P is a function P :A→ [0,1] with the following properties
P(∅) = 0. (2.2)
P(Ek),∀E1,E2, · · · ∈ A. (2.3)
assuming the events E1,E2, . . . are pairwise disjoint (mutually exclusive), and the triple (Ω ,A,P) is called a measure space. If in addition
P(Ω ) = 1, (2.4)
P is said to be a probability measure.
