Abstract
This Chapter provides a short introduction to measure theory and the theory of the Lebesgue integral. Avoiding as much as possible technical details, we present the basic ideas and also list the basic properties of measure and integral that will be used in this book. Let us note here that probability P(A) defined in Chapter 1 is nothing else but the measure of event A. Another basic probability concept, the mathematical expectation, established later in the book is nothing else but the integral with respect to the probability measure. To some extent, calculus of probability, theory of stochastic processes (including stochastic differential equations) and mathematical statistics can be thought of as parts of the theory of measure and integration.
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© 2002 Springer-Verlag Berlin Heidelberg
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Cyganowski, S., Kloeden, P., Ombach, J. (2002). Measure and Integral. In: From Elementary Probability to Stochastic Differential Equations with MAPLE®. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56144-3_2
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DOI: https://doi.org/10.1007/978-3-642-56144-3_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42666-0
Online ISBN: 978-3-642-56144-3
eBook Packages: Springer Book Archive