Is it true that a function is Riemann integrable on a bounded interval only if it's equal to a continuous function almost everywhere? I'd imagine this is the case, given the Riemann-Lebesgue lemma, which says that a function is RI iff its set of discontinuities has measure zero. (So the "continuous function" is then just f restricted to the complement of its set of discontinuities.) But I might be wrong. Help?(adsbygoogle = window.adsbygoogle || []).push({});

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Riemann integrable functions continuous except on a set of measure zero?

Loading...

Similar Threads - Riemann integrable functions | Date |
---|---|

A function f that is not Riemann integrable but |f| is Riemann integrable? | Aug 10, 2011 |

Riemann integrability of composite functions | Sep 26, 2010 |

Is the characteristic function of the irrationals Riemann integrable on [a,b]? | Feb 17, 2009 |

Complex Riemann-Stieltjes integral with a step function for integrator | Jan 17, 2009 |

Riemann-integrable functions | Oct 8, 2008 |

**Physics Forums - The Fusion of Science and Community**