A consideration of the Riemann-Stieltjes integral for complex-valued functions defined on a real closed interval

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Thomas Blair Clark (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/
E. E. Posey

Abstract: In view of the fact that most treatments of the Riemann-Stieltjes integral usually consider only real-valued functions, and whereas, complex-valued functions of a certain type are closely related to real-valued functions, it is the purpose of this thesis to demonstrate explicitly how the theory of Riemann-Stieltjes inteqration for complex-valued functions is developed. The development of the complex theory follows the same general pattern as the real case. In fact, the natural extensions of the latter are obvious after some preliminary results are shown. One result demonstrates clearly how the inteqral for complex-valued functions may be computed by expressing the integral in terms of real-valued functions. The final theorem is a special case in which the integration technique takes on the exact form of the real case.

Additional Information

Language: English
Date: 1971
Riemann integral
Functions of complex variables
Functions of real variables

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