http://repository.aust.edu.ng/xmlui/handle/123456789/442 This collection contains master's Theses of Pure and Applied Mathematics from 2009 to 2024. 2026-04-24T13:58:13Z http://repository.aust.edu.ng/xmlui/handle/123456789/5168 FINITE DIMENSIONAL GAUSSIAN MEASURES :PROBABILITY LAW APPROACH AND FUNCTIONAL APPROACH Abdullahi, Haruna Itopa In this thesis work, several notions from Functional analysis, Topology, Measure theory, and integration are used in the study of Gaussian measures in fi nite dimensions. We discussed this using the probability law approach and functional analysis approach. For the probability law frame, we began by introducing the Random vectors where we vividly talked about the Gaussian random vectors in which the Orthogonal matrices were a very important tool for the discourse. Here, we discussed enough content and results of the fi nite dimensional Gaussian measures which aids us to move to functional frame. For the functional frame, as the name implies, we re-frame the study and properties of Gaussian measures using notions of functional analysis where the Hermite polynomials both in one dimension and multi-dimension were introduced. We fi nally introduced the Ornstein Uhlencbeck Semi-group and one of its applications in Integro-differential equations. 2017-12-18T00:00:00Z http://repository.aust.edu.ng/xmlui/handle/123456789/5136 The Auman Integral of Set-Valued Maps Eleh, Chinedu Anthony This thesis focuses on the Aumann integral of set-valued random variables and its properties. We started o by studying the space in which this integral lies: hyperspace endowed with the Hausdor metric. We considered convergence on a hyperspace with respect to the Hausdor metric and reviewed the works of Kuratowski, Mosco in trying to abstract topologically, the Hausdor convergence; this led to a comparison between weak, Wijsmann, Kuratowski-Mosco convergences to Hausdor convergence. We proceeded to see the conditions under which a set-valued random variable is measurable, integrable and integrably bounded. Finally, we de ned the class of integrable selections of an integrable set-valued random variable and used it to de ne the Aumann integral, and went further to prove and outline su cient conditions for the Aumann integral to be convex and closed-valued respectively Main Thesis 2018-05-15T00:00:00Z http://repository.aust.edu.ng/xmlui/handle/123456789/5126 Co−Semigroups of Contradiction on Banach Spaces and Applications Isedowo, Joshua Wale Let X be a Banach space and A : D(A) ⊂ X −→ X be an unbounded linear operator on X. We study the concept of C0−semigroup of contraction on arbitrary Banach space X and give the two characterizations of A called infinitesimal generator of C0−semigroup on X namely, Hille-Yosida and Lumer Phillips characterizations. In the later part, we apply the approach of C0−semigroups to some partial differential equations with boundary conditions. Main Thesis 2023-03-17T00:00:00Z http://repository.aust.edu.ng/xmlui/handle/123456789/5125 Measurable Set-Valued Functions and Bochner Integrals Eze, Leonard Chidiebere In this thesis, several concepts from Topology, Measure Theory, Probability Theory, and Functional analysis were combined in the study of the measurability of set-valued functions and the Bochner integral. We started with a detailed study of the Hausdorff metric, its properties, and topology by exposing separately the case where E is a metric space and the case where E is a normed linear space. After reviewing the important theorems, we present the four convergences related to Hausdorff metric: Hausdorff convergence, Wisjman convergence, Weak convergence, and Kuratowski-Mosco convergence; and then compared them. Further, set-valued random variables and their properties were studied. We study and compare five types of measures of set-valued functions and the two forms of Bochner integral, that is, the Banach-valued and set-valued Bochner integrals. 2017-12-12T00:00:00Z