Predictability, entropy and information of infinite transformations
نویسندگان
چکیده
منابع مشابه
Predictability, Entropy and Information of Infinite Transformations
We show that a certain type of conservative, ergodic, measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also consider distribution asymptotics of information; e.g. for Boole’s transformation, information is asymptotically mod-normal, a property shared by certain ergodic, probability preserving transformations with zero entropy. §0 Intr...
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The Kolmogorov-Sinai entropy is a far reaching dynamical generalization of Shannon entropy of information systems. This entropy works perfectly for probability measure preserving (p.m.p.) transformations. However, it is not useful when there is no finite invariant measure. There are certain successful extensions of the notion of entropy to infinite measure spaces, or transformations with ...
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متن کاملar X iv : 0 70 5 . 21 48 v 5 [ m at h . D S ] 1 6 Ja n 20 09 PREDICTABILITY , ENTROPY AND INFORMATION OF INFINITE TRANSFORMATIONS
We show that a certain type of quasi finite, conservative, ergodic , measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also construct a conservative, ergodic , measure preserving transformation which is not quasi finite; and consider distribution asymptotics of information showing that e.g. for Boole’s transformation, information is as...
متن کاملar X iv : 0 70 5 . 21 48 v 4 [ m at h . D S ] 6 A pr 2 00 8 PREDICTABILITY , ENTROPY AND INFORMATION OF INFINITE TRANSFORMATIONS
We show that a certain type of quasi finite, conservative, ergodic , measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also construct a conservative, ergodic , measure preserving transformation which is not quasi finite; and consider distribution asymptotics of information showing that e.g. for Boole’s transformation, information is as...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2009
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm206-0-1