ABSTRACT
We have chosen Kolmogorov’s axiomatic system (Ω, https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203742013/69a53f4e-97e6-48d7-bf94-69ab32e54fc6/content/f.tif"/>, P) [see (2.1.1)–(2.1.3)] as our model of probabilities. In the Kolmogorov model, the set Ω is interpreted as the set of all possible outcomes, the σ-algebra https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203742013/69a53f4e-97e6-48d7-bf94-69ab32e54fc6/content/f.tif"/> is interpreted as the set of all “observable” events, and the probability P(F) is interpreted as the degree of conviction we have that the event F occurs. In many situations we have a certain information about the outcomes, which allow us to decide if some (but usually not all) events have occurred or not. For instance, suppose that we meet our good friend Agatha at a horse race between the fourth and fifth run, and consider the following two events:
