Necessary and Sufficient Conditions for Integrability

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


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.


Continuous Function Limit Point Differentiable Function Bounded Function Open Interval 
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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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