Discrete Spectrum Transformations
نویسنده
چکیده
An important problem in ergodic theory is to find classifications of various types of measure preserving transformations. An example of this is the theorem of Ornstein that two Bernoulli shifts are isomorphic iff they have the same entropy. So a Bernoulli shift can be assigned a real number that completely determines its isomorphism type. Can this be done for other types of transformations? Perhaps not with real numbers, but possibly with other types of invariants. This type of problem fits into the framework of definable equivalence relations in descriptive set theory. In this setting, equivalence problems are classified by the invariants that must be assigned to determine an object up to the equivalence is being considered.
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