Using the ideas of abstract algebra, we introduce the basic concepts of
abstract probability theory that generalize the Kolmogorov's probability
theory, possibility theory and other theories that deal with uncertainty. Based
on abstract addition and multiplication, we define an abstract measure and
abstract Lebesgue integral. System of Kolmogorov's axioms is criticized, after
which we introduce an abstract probability measure and abstract conditional
probability, show that they have recognizable probability properties. In
addition, we define an abstract expected value operator as the abstract
Lebesgue integral and prove its properties.Comment: 12 page