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Type of Document	Dissertation
Author	Baez-Duarte, Luis
URN	etd-01132003-082706
Persistent URL	http://resolver.caltech.edu/CaltechETD:etd-01132003-082706
Title	Pointwise abelian ergodic theorems
Degree	PhD
Option	Mathematics
Advisory Committee	Advisor Name Title Unknown Committee Member
Keywords	None
Date of Defense	1964-12-01
Availability	unrestricted
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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