Probability Theory I

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Focusing on a modern approach to probability theory grounded in measure theory, this book serves as a rigorous introduction for advanced students in mathematics, physics, or natural sciences. It covers essential topics such as measures and probability spaces, random variables, sequences of random variables, and expectation. Designed for those with a background in multidimensional calculus, it includes practical solved exercises to reinforce learning. Originating from courses at the University of Bologna, it aims to lay the groundwork for further studies in stochastic processes and statistical inference.