THE LEBESGUE-STIELJES INTEGRAL AS APPLIED IN PROBABILITY DISTRIBUTION THEORY
NAVAL POSTGRADUATE SCHOOL MONTEREY CA
Pagination or Media Count:
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 measureable functions are set forth in the introduction. Chapter 2 is concerned with establishing a one to one correspondence between LebesgueStieljes measures and certain equivalence classes of functions which are monotone non decreasing and continuous on the right. In Chapter 3 the Lebesgue-Stieljes 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.
- Statistics and Probability