LAWS OF LARGE NUMBERS IN REAL AND ABSTRACT SPACES by THEOPHILUS OLABODE
LAWS OF LARGE NUMBERS IN REAL AND ABSTRACT SPACES by THEOPHILUS OLABODE
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Date
1979
Authors
OGUNYEMI, THEOPHILUS OLABODE
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Abstract
For 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.
Description
Thesis 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,
Keywords
LAWS, LARGE, NUMBERS, REAL, ABSTRACT, SPACES