Is it true in general that if [itex]f[/itex] is Lebesgue integrable in a measure space [itex](X,\mathcal M,\mu)[/itex] with [itex]\mu[/itex] a positive measure, [itex]\mu(X) = 1[/itex], and [itex]E \in \mathcal M[/itex] satisfies [itex]\mu(E) = 0[/itex], then(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\int_E f d\mu = 0

[/tex]

This is one of those things I "knew" to be true yesterday, and the day before, and the day before...but now I can't show it! I need to be able to bound that integral, somehow, by [itex]\mu(E)[/itex], but how? Using Holder's inequality? But don't I need to know that [itex]f\in L^2[/itex] or [itex]f\in L^\infty[/itex] to do that? Do I know either of those? I don't think so...

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

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

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

# Lebesgue integration over sets of measure zero

Loading...

Similar Threads for Lebesgue integration sets |
---|

I How to derive this log related integration formula? |

I An integration Solution |

B I Feel Weird Using Integral Tables |

B Methods of integration: direct and indirect substitution |

I Lebesgue Integral of Dirac Delta "function" |

**Physics Forums | Science Articles, Homework Help, Discussion**