This question comes from Theorem 16.3 of Bartle's "The Elements of Integration and Lebesgue Measure", in page 163. The condition [tex]E\subseteq A[/tex] is indeed needed in the proof of necessary condition, but I did not find its usage anywhere in the proof of sufficient condition, for example, [tex]m^*(E)<+\infty[/tex] can be obtained from [tex]m(A-H)=m^*(E)[/tex], [tex]A-H\subseteq E[/tex] can be deduced from [tex]A-E\subseteq H[/tex]. Although I checked several times, I'm not sure if I missed something. So, Could someone help me make sure if the condition [tex]E\subseteq A[/tex] can be safely removed from the [tex]\Leftarrow[/tex] part of the theorem (then it may be the case that [tex]E\not\subseteq A[/tex] albeit the part of(adsbygoogle = window.adsbygoogle || []).push({}); Ethat lies outside ofAhas zero measure)? Thanks!

This book is available online, but I cannot paste its link due to rules of this forum, you can find it at gigapedia.

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

Dismiss Notice

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!

# A question about Caratheodory condition.

Loading...

Similar Threads for question Caratheodory condition | Date |
---|---|

B Function rules question | Mar 17, 2018 |

B Question about a limit definition | Feb 27, 2018 |

A Angular Moment Operator Vector Identity Question | Feb 10, 2018 |

I A question regarding Logistic population model | Feb 1, 2018 |

Deriving functions relating to condition numbers | Mar 23, 2017 |

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