Mathematics

Bernoulli shifts and local density property

S. V. Tikhonov

Russian State University of Trade and Economics, Moscow

Abstract: We consider the property LocDen for the squaring map in the space of all measure preserving transformations and in the space of mixing transformations. It is proved that Bernoulli shifts with an infinite entropy do not possess this property.

Key words: mixing transformations, entropy, Bernoulli shift.

UDC: 517

Received: 21.01.2011

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2012, 67:1, 29–35

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