Baez-Duarte, Luis (1965) Pointwise abelian ergodic theorems. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-01132003-082706
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|
|Division:||Physics, Mathematics and Astronomy|
|Thesis Availability:||Public (worldwide access)|
|Defense Date:||1 December 1964|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||13 Jan 2003|
|Last Modified:||26 Dec 2012 02:27|
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