# Chapter 3. Limits and Continuity of Functions

Published Online: 26 MAR 2003

DOI: 10.1002/0471394882.ch3

Copyright © 2003 John Wiley & Sons, Inc.

Book Title

## Advanced Calculus with Applications in Statistics, Second Edition

Additional Information

#### How to Cite

Khuri, A. I. (2002) Limits and Continuity of Functions, in Advanced Calculus with Applications in Statistics, Second Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471394882.ch3

#### Publication History

- Published Online: 26 MAR 2003
- Published Print: 1 NOV 2002

#### Book Series:

#### Book Series Editors:

- David J. Balding,
- Peter Bloomfield,
- Noel A. C. Cressie,
- Nicholas I. Fisher,
- Iain M. Johnstone,
- J. B. Kadane,
- Louise M. Ryan,
- David W. Scott,
- Adrian F. M. Smith and
- Jozef L. Teugels

#### ISBN Information

Print ISBN: 9780471391043

Online ISBN: 9780471394884

- Summary
- Chapter

### Keywords:

- big O notation;
- convex function;
- intermediate-value theorem;
- inverse function;
- Jensen's inequality;
- Lipschitz continuity;
- little o notation;
- loss function;
- risk function;
- uniform continuity

### Summary

The concepts of limits and continuity of real-valued functions, which are defined on the set of real numbers, are introduced in this chapter. Some properties associated with these concepts are discussed. Particular types of functions, such as convex and Lipschitz continuous functions, are also included. The chapter ends with a section giving examples of continuous and convex functions in statistics.