Measure, integral, and probability
By: Marek Capiński and Ekkehard Kopp.
Contributors: Kopp, P. E., 1944-
Series: Springer undergraduate mathematics series
Publisher: Springer
Published: 1999
Place of publication: London; New York
Language: eng
Number of pages: 227
Subjects: Measure theory; Integrals, Generalized; Probabilities
Description: The key concept is that of measure which is first developed on the real line and then presented abstractly to provide an introduction to the foundations of probability theory (the Kolmogorov axioms) which in turn opens a route to many illustrative examples and applications, including a thorough discussion of standard probability distributions and densities. Throughout, the development of the Lebesgue Integral provides the essential ideas: the role of basic convergence theorems, a discussion of modes of convergence for measurable functions, relations to the Riemann integral and the fundamental theorem of calculus, leading to the definition of Lebesgue spaces, the Fubini and Radon-Nikodym Theorems and their roles in describing the properties of random variables and their distributions. Applications to probability include laws of large numbers and the central limit theorem.
Notes: Includes bibliographical references (p. 223) and index.