The Lebesgue-Stieljes integral as applied in probability distribution theory.
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Authors
Van Sant, Thomas A.
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Date of Issue
1964
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Monterey California. Naval Postgraduate School
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en_US
Abstract
Necessary definitions and theorems from real variable dealing with some properties of Lebesgue-Stieljes measures, monotone non-decreasing
functions, Borel sets, functions of bounded variation and Borel measurable functions are set forth in the introduction. Chapter 2 is concerned with establishing a one to one correspondence between Lebesgue-Stieljes
measures and certain equivalence classes of functions which are monotone
non decreasing and continuous on the right. In Chapter 3 the LebesgueStieljes Integral is defined and some of its properties are demonstrated. In Chapter 4 probability distribution function is defined and the notions in Chapters 2 and 3 are used to show that the Lebesgue-Stieljes integral of any probability distribution function can be expressed as a countable sum of positive numbers added to the Lebesgue-Stieljes integral of a continuous probability distribution function. The conclusion indicates how the Lebesgue-Stieljes integral may be used to define the probability associated with a Borel set of real numbers.
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Thesis
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Department of Mathematics and Mechanics
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.