Based on the notions of measure spaces and measurable maps, we introduce the integral of a measurable map with respect to a general measure. This generalises the Lebesgue integral that can be found in textbooks on calculus. Furthermore, the integral is a cornerstone in a systematic theory of probability that allows for the definition and investigation of expected values and higher moments of random variables.
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Keywords
- Normal Representation
- Monotone Convergence
- Monotone Convergence Theorem
- Nonnegative Measurable Function
- Lebesgue Integrable Function
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© 2008 Springer-Verlag London Limited
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(2008). The Integral. In: Probability Theory. Universitext. Springer, London. https://doi.org/10.1007/978-1-84800-048-3_4
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DOI: https://doi.org/10.1007/978-1-84800-048-3_4
Publisher Name: Springer, London
Print ISBN: 978-1-84800-047-6
Online ISBN: 978-1-84800-048-3
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