Abstract
A real-valued function F(x), defined for all real x, is termed a 1-dimensional cumulative distribution function (c.d.f.) iff it satisfies the following four basic properties:
Cumulative distribution functions are fundamental, and our concern here is with certain Mathematical properties of c.d.f.’s that will be useful later when studying Bounded Variation Functions and the Riemann-Stieltjes Integral.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References to Additional and Related Material: Section 8
Feller, W., “An Introduction to Probability Theory and its Applications”, Vol. II, Wiley and Sons, New York (1966).
Hobson, E., “Theory of Functions of a Real Variable”, Vol. I, Dover Publications, Inc., New York.
McShane, E. and T. Botts, “Real Analysis”, VanNostrand, Inc., New York (1959).
Royden, H., “Real Analysis”, Macmillan Co., New York (1964).
Simmons, G., “Topology and Modern Analysis”, McGraw-Hill, Inc., New York (1963).
Titchmarsh, E., “The Theory of Functions”, (Second Ed.), Oxford University Press, (1939).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1979 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Meyer, R.M. (1979). 1-Dimensional Cumulative Distribution Functions and Bounded Variation Functions. In: Essential Mathematics for Applied Fields. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8072-6_8
Download citation
DOI: https://doi.org/10.1007/978-1-4613-8072-6_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90450-4
Online ISBN: 978-1-4613-8072-6
eBook Packages: Springer Book Archive