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This book is concerned with both the theory of the Kurzweil-Henstock integral and the basic facts on Riesz spaces. Moreover, even the so-called Sipos integral, which has several applications in economy, is illustrated. The aim of this book is two-fold. First, it can be understood as an introductory textbook to the Kurzweil-Henstock integral as well as to some algebraic structures which are important from the viewpoint of applications to integration and probability theory. Second, it discusses some possibilities of further developments including recent results and open problems.

The reference considers probability theory in two main domains: fuzzy set theory, and quantum models. Readers will learn about the Kolmogorov probability theory and its implications in these two areas.Other topics covered include intuitionistic fuzzy sets (IF-set) limit theorems, individual ergodic theorem and relevant statistical applications (examples from correlation theory and factor analysis in Atanassov intuitionistic fuzzy sets systems, the individual ergodic theorem and the Poincar� recurrence theorem).This book is a useful resource for mathematics students and researchers seeking information about fuzzy sets in quantum spaces.