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What is the textbook where the following simple fact can be found:

A measure defined on a semi-algebra S can be extended to a sigma-algebra generated by S.

In the texbooks that I have looked into the theory of measures is done without semi-algebras (for examlple Halmos deals with measures using hereditary sigma-rings). However, it is convenient for my applications to use the above simple fact.

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    $\begingroup$ Check Royden's book. $\endgroup$
    – Michael Renardy
    Jun 3, 2016 at 17:51
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    $\begingroup$ Does this really need a reference? For use in a paper, I'd consider it general knowledge, and just cite it as "Carathéodory's extension theorem". $\endgroup$
    – Nate Eldredge
    Jun 3, 2016 at 20:11
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    $\begingroup$ @MichaelRenardy: Yes, it's in there: Section 17.5 in the fourth edition. $\endgroup$
    – Nate Eldredge
    Jun 3, 2016 at 21:23
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    $\begingroup$ Someone should post this as an answer, for visibility $\endgroup$
    – Yemon Choi
    Jun 3, 2016 at 22:55
  • $\begingroup$ Thank you for those answers, I couldn't find it in the third edition of Royden, but it is in the fourth edition. $\endgroup$
    – Janusz Przewocki
    Jun 11, 2016 at 11:50

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