Convergenza di variabili casuali

This thesis delves into the critical concept of convergence of random variables in probability theory because convergence plays a pivotal role in core theorems like the central limit theorem. To enhance understanding, we have stated some properties and lemmas that lay the groundwork for our central topic. We started by talking extensively about the different models of convergence: almost sure convergence, convergence in probability, convergence in the r-th mean, and convergence in distribution, providing a definition and an example for each of them. The discussion was then tilted toward the relationships among them, utilising counterexamples for clarity. Lastly, we have discussed prominent theorems related to convergence models and the laws that derive directly from them, highlighting their applications: the strong law of large numbers, the weak law of large numbers, and the central limit theorem.