On unbounded probability theory

The value of the empirical expectation coincides with that of the mean energy of an ideal Bose gas for one particle. The exact mathematical identity for these quantities makes it possible to carry over the concept of temperature corresponding to the mean energy to an unboundedly increasing sequence of random values for a new unbounded probability theory and for a generalization of Kolmogorov complexity theory. The notion of spectral gap, which was introduced in superconductivity theory, is carried over to unbounded probability theory.