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In an article by G.C Rota, i read (page 8 of www-groups.dcs.st-and.ac.uk/history/Extras/rota.pdf):

"in Euclidean $n$-dimensional space there are exactly $n + 1$ invariant measures, namely, the Euler characteristic and the intrinsic volumes corresponding to the $n$ elementary symmetric functions. The discovery of this fact is an achievement of mathematics in the latter half of the twentieth century."

What is the theorem he is referring to?

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    Can you give a reference to the article? I have found similar remarks, but not this exact quotation, in [*Geometric Probability*](http://dx.doi.org/10.1007/BF03025223) which cites [*Introduction to Geometric Probability*](https://books.google.de/books?id=Q1ytkNM6BtAC) which mentions *Hadwiger's characterization theorem* in what little context Google Books offers. Perhaps [*Vorlesungen Über Inhalt, Oberfläche und Isoperimetrie*](https://books.google.de/books?id=_kimBgAAQBAJ) is the right reference? I suggest you look these up in a library with full access, if possible. – 2017-01-17
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    (also added at question-text) the quotation is at http://www-groups.dcs.st-and.ac.uk/history/Extras/rota.pdf, page 8 – 2017-01-17

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