Elementary fundamentals of a more general probability theory. I: Interval probability as comprehensive conception. In cooperation with T. Augustin and A. Wallner (Q2723272)

In this monograph the author presents a thorough treatment of the axiomatic foundations of interval probability theory. Interval probabilities attribute to each event an interval of numbers in the unit interval. When the intervals are degenerate one obtains Kolmogorov's approach while, on the other hand, in the case of an interval, this may be interpreted as one's subjective belief of a probability. The book consists of four chapters and an appendix. Chapter 1 presents some discussion of the various historical concepts of probability and a comprehensive motivation of the present approach. Chapter 2 is on totally determined probability, introducing \(R\)- and \(F\)-probability. Chapter 3 is on partially determined probability, while Chapter 4 discusses finite sample spaces. The book contains no exercises, but many examples in the text are well designed to make this book a welcome introduction to the area of interval probability.