In this chapter, we lay the measure theoretic foundations of probability theory. We introduce the classes of sets (semirings, rings, algebras, σ-algebras) that allow for a systematic treatment of events and random observations. Using the measure extension theorem, we construct measures, in particular probability measures on σ-algebras. Finally, we define random variables as measurable maps and study the σ-algebras generated by certain maps.
CITATION STYLE
Klenke, A. (2008). Basic Measure Theory. In Probability Theory (pp. 1–48). Springer London. https://doi.org/10.1007/978-1-84800-048-3_1
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