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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?

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?

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?

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Point mapping induces a set mapping

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?