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 generalizes 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.
CITATION STYLE
Klenke, A. (2014). The Integral (pp. 85–99). https://doi.org/10.1007/978-1-4471-5361-0_4
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