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I am currently reading a book about fractals and the author states the result that Hausdorff measure is semifinite. Can someone tell me how to prove or provide a hint for me?

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What does "semifinite" mean? –  Chris Eagle Feb 26 '13 at 15:45
    
For every measurable set A which has infinite measure,there exists a subset B of A,which has positive finite measure. –  Ben Feb 26 '13 at 15:55
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This is not easy, and I would not want to reproduce the proof here. See Theorem 8.19 in Geometry of Sets and Measures in Euclidean Spaces by Pertti Mattila. –  user53153 Feb 26 '13 at 19:54

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