Pointwise Abelian Ergodic Theorems

Citation

Baez-Duarte, Luis (1965) Pointwise Abelian Ergodic Theorems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/QZGT-A511. https://resolver.caltech.edu/CaltechETD:etd-01132003-082706

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. Let [...] be a measure space, and T a positive contraction of [...]. Let [...] be a sequence of non-negative numbers whose sum is one, and [...] a sequence defined by inductions as follows [...]. Now let [...], then we prove in this work that [...] exists almost everywhere in the set [...]. When [...] we get that all [...]. In this case (*) yields the abelian analog of the well-known ergodic theorem of Chacon-Ornstein dealing with the convergence of averages of the form [...] whose proof we have generalized and adapted to show the convergence of [...]. We have also considered the generalization of (**) to weighted averages [...] whose convergence in [...] was recently proved by G. E. Baxter. We have given a considerably simpler proof for this fact.

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