Abstract
This chapter studies the notion of measurable partition in detail. As far as we know, there exists no elementary treatise of this notion, and yet it plays an important role in ergodic theory. We have seen it play a role in Chap. 14 when we studied the decomposition of a transformation into ergodic components.
The title of Rokhlin’s paper [On the fundamental ideas of measure theory] seems to suggest that measurable partitions are the main object of measure theory. But probably this would seem very doubtful to most analysts (“all my life I have worked with the Lebesgue integral, and this is the first time I have heard about measurable partitions”). D.V. Anosov
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Coudène, Y. (2016). Measurable Partitions and σ-Algebras. In: Ergodic Theory and Dynamical Systems. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-7287-1_15
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DOI: https://doi.org/10.1007/978-1-4471-7287-1_15
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