Bernoulli shifts and property of local density / S. V. Tikhonov. //Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2012. ? 1. P. 31-37 [Moscow Univ. Math. Bulletin. Vol. 67, N 1, 2012.].

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.