# Is Hahn-Kolmogorov theorem a direct result of Carathéodory's extension theorem?

Both theorems assume the same condition and conclusion, except that

Since a field of subsets is also a ring of subsets, is Hahn-Kolmogorov theorem a direct result of Carathéodory's extension theorem?

Thanks!

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Hahn-Kolmogorov could be seen as the small brother to Caratheodory, that is it is slightly more direct but for the price of requiring a little bit more assumptions and getting less further... Moreover, Caratheodory is sort of an upgrade of the idea of Hahn-Kolmogorov. –  Freeze_S Sep 7 '14 at 2:14