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
收藏
页码：301 / 344
页数：44
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