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Probability, Fourth Edition by Rick Durrett

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1Measure Theory

In this chapter, we recall some definitions and results from measure theory. Our purpose here is to provide an introduction for readers who have not seen these concepts before and to review that material for those who have. Harder proofs, especially those that do not contribute much to one’s intuition, are hidden away in the Appendix. Readers with a solid background in measure theory can skip Sections 1.4, 1.5, and 1.7, which were previously part of the Appendix.

1.1 Probability Spaces

Here and throughout the book, terms being defined are set in boldface. We begin with the most basic quantity. A probability space is a triple (Ω, , P) where Ω is a set of “outcomes,” is a set of “events,” and P : → [0, 1] is a function that assigns ...

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