Integration in a Probability Space

Yuan Shih Chow and Henry Teicher
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Yuan Shih Chow: Columbia University, Department of Mathematics and Statistics
Henry Teicher: Rutgers University, Department of Statistics

Chapter 4 in Probability Theory, 1978, pp 83-109 from Springer

Abstract: Abstract There are two basic avenues to integration. In the modern approach the integral is introduced first for simple functions—as a weighted average of the values of the function—and then defined for any nonnegative measurable function f as a limit of the integrals of simple nonnegative functions increasing to f. Conceptually this is extremely simple, but a certain price is paid in terms of proofs. The alternative classical approach, while employing a less intuitive definition, achieves considerable simplicity in proofs of elementary properties.

Keywords: Random Walk; Probability Space; Simple Random Walk; Monotone Convergence Theorem; Markov Inequality (search for similar items in EconPapers)
Date: 1978
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DOI: 10.1007/978-1-4684-0062-5_4

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