Measure theory is the study of measures. It generalizes the intuitive notions of length, area, and volume. The earliest and most important examples are Jordan measure and Lebesgue measure, but other examples are Borel measure, probability measure, complex measure, and Haar measure.
Measure Theory
See also
Almost Everywhere Convergence, Cantor Set, Fatou's Lemma, Fractal, Integral, Integration, Lebesgue's Dominated Convergence Theorem, Measurable Function, Measurable Set, Measurable Space, Measure, Measure Space, Monotone Convergence Theorem, Pointwise ConvergenceThis entry contributed by John Derwent
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References
Doob, J. L. Measure Theory. New York: Springer-Verlag, 1994.Evans, L. C. and Gariepy, R. F. Measure Theory and Fine Properties of Functions. Boca Raton, FL: CRC Press, 1992.Gordon, R. A. The Integrals of Lebesgue, Denjoy, Perron, and Henstock. Providence, RI: Amer. Math. Soc., 1994.Halmos, P. R. Measure Theory. New York: Springer-Verlag, 1974.Henstock, R. The General Theory of Integration. Oxford, England: Clarendon Press, 1991.Kestelman, H. Modern Theories of Integration, 2nd rev. ed. New York: Dover, 1960.Kingman, J. F. C. and Taylor, S. J. An Introduction to Measure and Probability. Cambridge, England: Cambridge University Press, 1966.Rao, M. M. Measure Theory And Integration. New York: Wiley, 1987.Stroock, D. W. A Concise Introduction to the Theory of Integration, 2nd ed. Boston, MA: Birkhäuser, 1994.Weisstein, E. W. "Books about Measure Theory." http://www.ericweisstein.com/encyclopedias/books/MeasureTheory.html.Referenced on Wolfram|Alpha
Measure TheoryCite this as:
Derwent, John. "Measure Theory." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/MeasureTheory.html