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Pointwise abelian ergodic theorems

Baez-Duarte, Luis (1965) Pointwise abelian ergodic theorems. Dissertation (Ph.D.), California Institute of Technology. http://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.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Major Option:Mathematics
Thesis Committee:
  • Unknown,
Defense Date:1 December 1964
Record Number:etd-01132003-082706
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-01132003-082706
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:146
Collection:CaltechTHESES
Deposited By: Imported from ETD-db
Deposited On:13 Jan 2003
Last Modified:25 Dec 2012 14:57

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