SPATIAL-TEMPORAL DIFFERENTIATION THEOREMS

被引：0

作者：

Assani, I ^{[1
]}

Young, A. ^{[1
]}

机构：

[1] Univ N Carolina, Chapel Hill, NC 27599 USA

来源：

ACTA MATHEMATICA HUNGARICA | 2022年 / 168卷 / 02期

关键词：

spatial-temporal differentiation; dynamical system; ergodic theorem; uniquely ergodic system; strong law of large numbers;

D O I：

10.1007/s10474-022-01276-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let (X,B,mu,T) be a dynamical system where X is a compact metric space with Borel sigma-algebra B, and mu is a probability measure that is ergodic with respect to the homeomorphism T: X -> X. We study the following differentiation problem: Given f is an element of C(X) and F-k is an element of B, where mu(F-k) > 0 and mu(F-k) -> 0, when can we say that (lim )(k ->infinity)integral(Fk)(1/k( )Sigma(k-1)(i=0)T(i)f)d mu/mu(F-k) = integral fd(mu) ? We establish some sufficient conditions for these sequences to converge.

引用

页码：301 / 344

页数：44

共 11 条

[1] APPLICATION OF NUMBER-THEORY TO ERGODIC-THEORY AND THE CONSTRUCTION OF UNIQUELY ERGODIC MODELS
BELLOW, A
FURSTENBERG, H
[J]. ISRAEL JOURNAL OF MATHEMATICS, 1979, 33 (3-4) : 231 - 240
[2] Dajani K., 2002, ERGODIC THEORY NUMBE
[3] Eisner T., 2015, Operator Theoretic Aspects of Ergodic Theory
[4] Folland GB., 1999, REAL ANAL
[5] Goodman T.N.T., 1971, B LOND MATH SOC, V3, P176
[6] ERGODICITY, UNIFORMITY AND UNIQUE ERGODICITY
HANSEL, G
RAOULT, JP
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1973, 23 (03) : 221 - 237
[7] Ergodic optimization
Jenkinson, O
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2006, 15 (01) : 197 - 224
[8] JEWETT RI, 1970, J MATH MECH, V19, P717
[9] ON ENTROPY AND GENERATORS OF MEASURE-PRESERVING TRANSFORMATIONS
KRIEGER, W
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 149 (02) : 453 - &
[10] Strong orbit realization for minimal homeomorphisms
Ormes, NS
[J]. JOURNAL D ANALYSE MATHEMATIQUE, 1997, 71 (1): : 103 - 133

← 1 2 →