Web Derivatives
Hewitt Kenyon · Anthony Perry Morse
Jan 1973 · American Mathematical Society: Memoirs of the American Mathematical Society Ibhuku elingu-132 · American Mathematical Soc.
I-Ebook
177
Amakhasi
reportIzilinganiso nezibuyekezo aziqinisekisiwe Funda Kabanzi
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After some measure-theoretic preliminaries, the notion of web is defined and used to construct a dimension- and metric-free setting for the differentiation of non-negative valued set functions. Conditions which guarantee the frequent existence of the derivative of one such function with respect to another are examined in detail, and then strengthened to permit integration of the derivative in case the denominator function is a measure. A Lebesgue decomposition of a function into a part which is the integral of its derivative and a remainder with derivative almost everywhere zero is obtained. The resulting theory is applied to differentiation of indefinite integrals, complex valued functions of bounded variation on the reals, and others.
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