Mathematics is the universal language.
That is, until someone says the word "obvious", or "well known". At which point it becomes relative to the reader.
My question is about a "well known" theorem. My problem is that it is not known to me. But I would like to know.
The following comes from Y. Katznelson and B. Weiss The Classification of Non-Singular Actions, Revisited, J. Ergodic Theory and Dynamical Systems, 11, 1991. Page 4.
It reads:
Thus the family {$\theta_k$} defines a Boolean set mapping between the $\sigma$-algebras generated by the ladder sets. If the ladder sets are both "algebra complete", a well known theorem implies that there exists a point mapping $\theta : X \mapsto X^\prime$ which induces a set mapping.
Can someone please tell me which theorem they are referring to here?
${\theta_k\}$defines a mapping of Boolean algebras $B \to B'$. The theorem you are looking for is probably something along the lines of: given a mapping of Boolean algebras $B\to B'$ where $B$ and $B'$ are $\sigma$-algebras of finite measure spaces $X$ and $X'$ resp., one has a map $X\to X'$ of the underlying sets (finite because this is what the authors assume). Finiteness here makes this much easier. But I'm not an expert in this field. – David Roberts Aug 26 2011 at 2:07