算子族的遍历镜像收敛推导

Operator Families Through Images Derived Convergence

现代分析学中，运用算子族的点态收敛性导出了Lebesgue微分定理。起支撑作用的遍历定理有Birklhoff-Khinchin点态遍历定理，von Neumann平均遍历定理、wiener控制遍历定理。本文深入运用算子族的收敛性导出新结论，拟命名为遍历镜像收敛定理．本质上，镜像遍历定理一方面将上述三大遍历定理进行综合与拓展，另一方面揭示了遍历算子族的反演收敛特性，使得算子族的收敛性使用范围更广更深。

In modem analytical science, the use of the pointwise operator family derived Lebesgue convergence theorem of differential. Play a supportive role with Birklhoff-Khinchin ergodic theorem pointwise ergodic theorem, von Neumann mean ergodic theorem, Wiener control ergodic theorem. This in-depth use of operators to derive new convergence family of conclusions to be named through the mirror convergence theorem. In essence, the mirror through one of the above three theorems Ergodic Theorem comprehensive and expand on the other hand reveals the family through the inversion operator convergence, which makes the convergence of the operator family use broader and deeper.