一致Lipschitz映射的遍历定理及其遍历分解

Ergodic theorem and ergodic decomposition for uniform Lipschitz mappings.

设(X,d)是一个可分的度量空间,Cu(X,d)是由全体一致连续函数所组成的C(X,d)的子空间,T是定义UkTf在Cu(X)上收敛.从这个基本结果出发,利用Cu(X,d)在X上的一致Lipschitz映射,那么对f∈Cu(X),1n∑nk=1的共扼空间的表示定理,得到了相空间的Yosida型遍历分解;利用空间的嵌入技术证明了非一致Lipschitz映射的大数法则.

If (X,d) is a separable metric space, C_u(X,d) the subspace of all uniformly continuous functions of (C(X,d),) T a uniform Lipschitze mapping defined on X. Then for f∈C_u(X),1n∑nk=1U^k_Tf converges in C_u(X). From this basic result the Yosida-like ergodic decomposition of the phase space using the representation of conjugate space for C_u(X) is obtained; The law of large numbers for non-Lipschitze mappings is also proved by means of embedding technique of space.