Date of Submission

2-28-1977

Date of Award

2-28-1978

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Mathematics

Department

Economic Research Unit (ERU-Kolkata)

Supervisor

Maitra, Ashok (ERU-Kolkata; ISI)

Abstract (Summary of the Work)

Current interest in the descriptive theory of sc ts stems largely from the many applications that the classical theory has found in probability theory, functional analysis, dynanic programming etc. As exarples, we cite the fundament al paper of Blackwell 15J wherein he has shown that many of the pathologies of probability theory c an be avoided if one takes the basic probability space to be an analytic set. As another example, we mention that several vritere [7), L23] have shown that in Blackwell's model of dynamic programming 131 the existence of optimal strategies ig related to the cxistence of measurable selectors.The present thesis is partly motivated by probl ems relating to the theory of Borel and analytic sets that have the ir origin in the papers referred to above. However wo wish to point out that the probleme considered in the thesis are of independent interest in the descriptive theory of sets without reference to their applicationa in the ficlds mentioned above.Chaptere 1-3 deal with the cxistence of measurable selectors in a wide variety of situations. Chapter 6 deals with A-functions. Such functions arise naturallv in probleme Chaptere 1-3 deal with the cxistence of measurable selectors in a wide variety of situations. Chapter 6 deals with A-functions. Such functions arise naturally in probleme of dynamic programming, see, for examplo, 17J. Chapter 4 of CvS POFC -II- deals with the class of measurable spaces that have come to be called Blackwell spaces. Such spaces are an a bstraction of a property of analytic spaces noted by Blackwell in 15). Chapter 5 deals with the complementation problem in the lattice of sub o-fields of the Borel o-fiela, a study which was initiated by D. Basu [21 in connection with problems of statistics and subfields.Below we summarize the main results of the thesis. The first chap ter deals with selection theorems for Multifunctions.The main result is the following.

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:28842964

Control Number

ISILib-TH40

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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