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- W4243470780 abstract "This chapter introduces the integral of measurable functions. This concept is fundamental also for probability theory, because the expectation of a numerical random variable with respect to a probability measure is the integral of a measurable function with respect to a probability measure. The chapter starts with defining the integral of a measurable function with respect to a measure μ. Then it explains the most important rules of computation and other properties of integrals, introduces the concept of a measure with density, and treats the relationship between the Riemann integral and the integral with respect to the Lebesgue measure. Next, the chapter focuses on absolute continuity and the Radon-Nikodym theorem. Both issues are crucial for conditional expectations. Finally, the chapter focuses on the integral with respect to a product measure." @default.
- W4243470780 created "2022-05-12" @default.
- W4243470780 date "2017-03-10" @default.
- W4243470780 modified "2023-09-25" @default.
- W4243470780 title "Integral" @default.
- W4243470780 doi "https://doi.org/10.1002/9781119243496.ch3" @default.
- W4243470780 hasPublicationYear "2017" @default.
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