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.
KeywordsNormal Representation Monotone Convergence Monotone Convergence Theorem Nonnegative Measurable Function Lebesgue Integrable Function
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