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Necessary and Sufficient Conditions for Integrability

  • Edwin E. Moise
Part of the Universitext book series (UTX)

Abstract

Every continuous function [a,b] →ℝ is uniformly continuous. There are three natural proofs of this theorem, using (a) The Nested Interval Theorem, (b) the Heine-Borel Theorem, and (c) the Bolzano-Weierstrass Theorem respectively.

Keywords

Continuous Function Limit Point Differentiable Function Bounded Function Open Interval 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 1982

Authors and Affiliations

  • Edwin E. Moise
    • 1
  1. 1.Department of Mathematics Queens CollegeCity University of New YorkFlushingUSA

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