Citation
BaezDuarte, Luis (1965) Pointwise abelian ergodic theorems. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd01132003082706
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 nonnegative 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 wellknown ergodic theorem of ChaconOrnstein 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 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Mathematics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  1 December 1964 
Record Number:  CaltechETD:etd01132003082706 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd01132003082706 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  146 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  13 Jan 2003 
Last Modified:  26 Dec 2012 02:27 
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