LAWS OF LARGE NUMBERS IN REAL AND ABSTRACT SPACES by THEOPHILUS OLABODE

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dc.contributor.authorOGUNYEMI, THEOPHILUS OLABODE
dc.date.accessioned2014-02-10T09:34:29Z
dc.date.available2014-02-10T09:34:29Z
dc.date.issued1979
dc.descriptionThesis submitted in partial fufilment of the requirements for the Master of Science in Department of Mathematics, Faculty of Science, Ahmadu Bello University, Z A R I A,en_US
dc.description.abstractFor most people the idea of probability is closely related to that of relative frequency. Therefore, it is natural that an attempt was made to construct a mathematical theory of probability using this concept. The results of the investigations on the relationship between probability and relative frequency are called the laws of the large numbers. At present, the development of laws of large numbers based on the initial attempt is going on with extreme intensity, the development has gone far beyond the study of random variables in the real space. Infact, the development has become established in some important abstract spaces. Having described briefly the stage of development of laws of large numbers, I now state the main purpose of this thesis: 1. To give a systematic review of the laws of large numbers in the real space. 2. To approach the proofs, in particular, on the strong laws of large numbers by the application of an important stochastic process - martingales. 3. To study the recent work on the laws of large numbers in some "well-behaved" abstract spaces, Hilbert space and general Banach spaces with "desirable" properties. III It is, however, ragretable that lack of materials on topological and geometrical properties of the abstract spa derestricts my urge of going deeper on (3) where the metric properties of normed spaces become a sophisticated tool in proving the law of large numbers. Finally, it should be remarked that references to books and papers given at the end of the thesis are indicated with [ ] in the course of the work.en_US
dc.identifier.urihttp://hdl.handle.net/123456789/776
dc.language.isoenen_US
dc.subjectLAWSen_US
dc.subjectLARGEen_US
dc.subjectNUMBERSen_US
dc.subjectREALen_US
dc.subjectABSTRACTen_US
dc.subjectSPACESen_US
dc.titleLAWS OF LARGE NUMBERS IN REAL AND ABSTRACT SPACES by THEOPHILUS OLABODEen_US
dc.typeThesisen_US
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