Probabilitats avançades

Abstract

[en] The aim of this work is to extend the concepts studied in the subject of Probabilities of the degree in mathematics. In order to delve into familiar notions and deal with new concepts, we link probability theory to measurement theory. This construction provides us with a mathematical framework and a coherent language that unifies different ideas and eliminates the need to distinguish between fundamentally similar objects. As we have introduced, we will cover familiar concepts such as distributions, expectation, integration of random variables, or independence, and some new ones, such as the extent of measures, the product of probability spaces, or the characteristic function. We will also present some fundamental results such as the convergence theorems, the Radon-Nikodym theorem, the strong law of large numbers or the central limit theorem, among others.