Pointwise Abelian Ergodic Theorems

Author: Baez-Duarte, Luis

Year: 1965

Degree: Dissertation (Ph.D.)

Advisor: Garsia, Adriano M.

Committee Member: Unknown, Unknown

Option: Mathematics

DOI: 10.7907/QZGT-A511

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.

Files