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Probability Measures: Fundamentals and Examples
This lecture covers the fundamentals of probability measures, defining a probability measure on a measurable space as a mapping to the interval [0, 1]. It explains properties of probability measures, such as finite additivity and examples of probability measures on different sets. The lecture also introduces Lebesgue measure on R and R², discussing its extension and notation. Terminology related to probability spaces and events is presented, including negligible and almost sure events. Propositions regarding negligible and almost-sure sets are discussed, highlighting the closure properties of these sets.