Abstract: On the basis of the theory of hyper-random phenomena, the calculus approaches for divergent and multiple-valued sequences and functions have been developed. For divergent sequences and functions, a number of new concepts, in particular concepts of generalized limit, spectrum of limit points, convergence to spectrum of limit points, distribution function and density function of limit points, bounds of a distribution function etc. are introduced. Concepts known for single-valued functions, in particular concepts of convergence, continuity, derivative, differentiability, indefinite and definite integrals are generalized on multiple-valued functions. A link between multiple-valued and divergent functions is found. Transformation particularities of single-valued functions into multiple-valued functions and multiple-valued functions into single-valued ones are researched.

Keywords: divergent function, partial limit, multiple-valued function, divergent integral, theory of hyper-random phenomena.

ACM Classification Keywords: G.3 Probability and Statistics

Link:

DIVERGENT AND MULTIPLE-VALUED SEQUENCES AND FUNCTIONS

Igor Gorban

http://foibg.com/ibs_isc/ibs-28/ibs-28-p43.pdf