Chapter 3. Limits and Continuity of Functions

  1. André I. Khuri

Published Online: 26 MAR 2003

DOI: 10.1002/0471394882.ch3

Advanced Calculus with Applications in Statistics, Second Edition

Advanced Calculus with Applications in Statistics, Second Edition

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

Author Information

  1. University of Florida, Gainesville, Florida, USA

Publication History

  1. Published Online: 26 MAR 2003
  2. Published Print: 1 NOV 2002

Book Series:

  1. Wiley Series in Probability and Statistics

Book Series Editors:

  1. David J. Balding,
  2. Peter Bloomfield,
  3. Noel A. C. Cressie,
  4. Nicholas I. Fisher,
  5. Iain M. Johnstone,
  6. J. B. Kadane,
  7. Louise M. Ryan,
  8. David W. Scott,
  9. Adrian F. M. Smith and
  10. Jozef L. Teugels

ISBN Information

Print ISBN: 9780471391043

Online ISBN: 9780471394884

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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.