n-Dimensional Riemann-Stieltjes Integral
We now generalize the results of Section 9 to consider the n-Dimensional (n > 1) Riemann-Stieltjes Integral with respect to an n-dimensional c.d.f., then, more generally, with respect to left-continuous n-dimensional b.v.f.’s. The development closely parallels that of the 1-dimensional case, and for this reason we will generally be briefer with proofs and descriptions than before. However, this by no means indicates that the n-dimensional Integral is any less important in applications.
Unable to display preview. Download preview PDF.
References to Additional and Related Material: Section 11
- 2.Gunther, N., “Sur les Integrales de Stieltjes”, Chelsea Publishing Company (1949).Google Scholar
- 3.Henstock, R., “Theory of Integration”, Butterworths (1963).Google Scholar
- 4.Hobson, E., “Theory of Functions of a Real Variable”, Vol. I, Dover Publications, Inc.Google Scholar
- 5.Kestelman, K., “Modern Theories of Integration”, Dover Publications, Inc.Google Scholar
- 6.Pesin, I., “Classical and Modern Integration Theories”, Academic Press (1970).Google Scholar
- 7.Zaanen, A., “An Introduction to the Theory of Integration”, North-Holland Publishing Co. (1958).Google Scholar