Accession Number : AD0764766

Title :   A Study and Comparison of the Stieltjes and Lebesgue-Stieltjes Integration Theories.

Descriptive Note : Master's thesis,

Corporate Author : AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OHIO SCHOOL OF ENGINEERING

Personal Author(s) : Gravelle,Robert Michael

Report Date : JUN 1973

Pagination or Media Count : 117

Abstract : A generalization of the Riemann integral commonly referred to as the Stieltjes integral is studied. The three definitions of this integral found in the literature are compared and found to be dissimilar. The most general of them, the 'Generalized Stieltjes' integral, is chosen for further study. Essential properties of this integral and criteria for establishing Stieltjes integrability (that is, whether the integral of a function over an interval assumes a finite value) are examined. Next, the Lebesgue-Stieltjes integral, a generalization of the Lebesgue integral, is studied. Essential properties of this integral are determined and criteria for establishing Lebesgue-Stieltjes integrability are established. Stieltjes and Lebesgue-Stieltjes integration are compared. (Modified author abstract)

Descriptors :   (*NUMERICAL INTEGRATION, THEOREMS), INTEGRALS, SET THEORY, MEASURE THEORY, MAPPING(TRANSFORMATIONS), THESES

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE