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Mar 11, 2013 at 23:31 comment added Santi Spadaro Hi Joel, thanks for the cute proof and the extensive references!
Mar 11, 2013 at 23:28 vote accept Santi Spadaro
Mar 11, 2013 at 0:38 comment added Joel David Hamkins Although the question only states as its hypothesis the implication that $A\in\mu\to f^{-1}A\in\mu$, in fact this implies the biconditional $A\in\mu\leftrightarrow f^{-1}A\in\mu$, since if $A\notin\mu$, then $X-A\in\mu$ and so $f^{-1}(X-A)\in\mu$, which is disjoint from $f^{-1}A$.
Mar 10, 2013 at 21:15 history answered Joel David Hamkins CC BY-SA 3.0