Date of Submission

2-28-1973

Date of Award

2-28-1974

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Mathematics

Department

Research and Training School (RTS)

Supervisor

Nadkarni, Mahendra G. (RTS-Kolkata; ISI)

Abstract (Summary of the Work)

This thesis consists of four chapters.The inpetus for the work in Chapter 1 comes from the concept of 'conditional atom' introduced by ileveu (191. Here, using conditional atoms we generalize the concept of nenatomicity of measures. (We confine ourselves to probability measures). We obtain generalizations of results on non atomic measures in [1), [3] and of Liapounoff's theorem. The results in Chapter 2 have their origins in a paper by Boylan [7]. To study 'e quiconvergence of martingales' Boylan introduced in [7] a metric on the space of complete sub d-algebras of a probability space. A little later, Never showed in [19 al, this metric space of complete sub o-algebras is 'tight ; that is, if two sub T-algebras are close under this metric with one contained in the other, than there is a set (a conditional atom), with high probability on which thetraces of thesed-algobras coincide, In Chapter 2 we investigate what else this metric space is besides being tight. We prove a host of results concerning the to phonological properties of this metric space; we also study an isomorphism problem.Chapters 3 and 4 are devoted to probloms in martingales. In Chapter 3 we prove a convergence theorem for airier with time process (a generalization due to Blake of martingalesin [5]). In Chapter 4 we disprove with the help of an exemple a conjecture on singular marting les mado by Luis Bacz-Duarto in [14].Some of tho results in this thesis have already appeared in print. Sec [23] and [24],

Comments

ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28842944

Control Number

ISILib-TH17

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

DOI

http://dspace.isical.ac.in:8080/jspui/handle/10263/2146

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