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The Riemann Integral II

  • Emanuel Fischer
Chapter
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

We now consider the legitimacy of passing to the limit under the integral sign. If the sequence 〈f n 〉 of R-integrable functions converges to a limit f on an interval [a, b] does it necessarily follow that
$$_{n \to \, + \,\infty }^{\lim }\int_a^b {{f_n}\left( x \right)dx = \int_a^b {f\left( x \right)dx?} }$$
(1.1)

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Copyright information

© Springer-Verlag New York, Inc. 1983

Authors and Affiliations

  • Emanuel Fischer
    • 1
  1. 1.Department of MathematicsAdelphi UniversityGarden CityUSA

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