On the structure of invariant measures for set-valued maps

被引：0

作者：

Gorbachev, A. N. ^{[1
]}

Stepin, A. M. ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Fac Mech & Math, Moscow, Russia

来源：

SBORNIK MATHEMATICS | 2011年 / 202卷 / 09期

关键词：

set-valued maps; invariant measure; Choquet simplex;

D O I：

10.1070/SM2011v202n09ABEH004187

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Properties of measures invariant with respect to set-valued maps are studied. It is shown that an absolutely continuous invariant measure for a set-valued map need not be unique, and the set of all invariant measures need not be a Choquet simplex. The problem concerning the existence of invariant measures with respect to set-valued maps parametrized by single-valued and set-valued maps of the circle having various smoothness classes is studied.

引用

页码：1285 / 1302

页数：18

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