Relative entropy tuples,relative u.p.e. and c.p.e. extensions |
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Authors: | Wen Huang Xiangdong Ye Guohua Zhang |
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Institution: | (1) Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, P.R. China;(2) Institut de mathématiques de Luminy, 163 Avenue de Luminy, case 907, 13288 Marseille cedex 9, France |
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Abstract: | Relative entropy tuples both in topological and measure-theoretical settings, relative uniformly positive entropy (rel.-u.p.e.)
and relative completely positive entropy (rel.-c.p.e.) are studied. It is shown that a relative topological Pinsker factor
can be deduced by the smallest closed invariant equivalence relation containing the set of relative entropy pairs. A relative
disjointness theorem involving relative topological entropy is proved. Moreover, it is shown that the product of finite rel.-c.p.e.
extensions is also rel.-c.p.e..
The first author is partially supported by NCET, NNSF of China (no. 10401031) and CNRS-K.C.Wong Fellowship.
The second author is supported by the national key project for basic science (973).
The third author is supported by NNSF of China (no. 10401031). |
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