The relativistic semigroup, the Lorentz group, and tachyons. III

Abstract

The algebraic and topological properties of the relativistic semigroup are discussed. Its probability-theoretical features establish that the relativistic semigroup belongs to the type of complex Markov structures. From the functional point of view, the relativistic semigroup is a compact Lie semigroup which is contracting in partial spaces. Principles of measurability, observability, and stochasticity are formulated, and these lead to a space-time structure of complex Markov kind. Thus, a certain probability-theoretical gnosiology is also possible in the theory of relativity.