Abstract
Kolmogorov probability theory based on set theory belongs to the most important results of mathematics of the 20th century. Naturally, its main advantage is the possibility to use results of the modern measure theory. However, this fact sometimes does not allow larger considerations. In this chapter we want to show this paradox can be eliminated. Of course, we present only some basic ideas. Understanding them enables one to study further results and applications.
Keywords: Probability, Measure, Measurable functions, Random variable, Lebesgue integral, Independence, Limit theorems, Conditional expectation, Limit laws for maxima, Peaks over threshold.
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