| CODE | SOR3111 | ||||||||
| TITLE | Measure and Integration Theory | ||||||||
| UM LEVEL | 03 - Years 2, 3, 4 in Modular Undergraduate Course | ||||||||
| MQF LEVEL | 6 | ||||||||
| ECTS CREDITS | 6 | ||||||||
| DEPARTMENT | Statistics and Operations Research | ||||||||
| DESCRIPTION | - Construction of Lebesgue measure on R - extension of the length of an interval - extension of volume on Rn - Extension of premeasures - from rings of subsets to ?-algebras - uniqueness of extensions - Caratheodory method using outer measure for general sets - Measure Spaces and Measurable Functions - Definitions - Vector lattice properties of the space of Measurable, real-valued Functions on a measure space - Integration - Definition of integrability - Integration of real-valued, measurable functions defined on general measure space - Monotone ConvergenceTheorem - Dominated Convergence theorems - Fatou's Lemma - Lp spaces - Vector lattice properties of the space of p'th integrable functions - Holder and Minkowski inequalities - Construction of Banach space of p-th integrable functions - Product Measures - Definition of measures and of integrability on products of measure spaces - Fubini Theorem Suggested texts: Shiryaev, A.N. (1996) Probability, Springer Bauer, H. (1981) Probability Theory and Elements of Measure Theory, Academic Doob, J.L. (1953) Stochastic Processes, Wiley Jacod, J. and Protter, P. (2000) Probability Essentials, Springer Taylor, S.J. (1973) Introduction to Measure and Integration, Cambridge Billingsley, P. (1995) Probability and Measure, Wiley Capinski, M. and Kopp, E., (2000) Measure, Integral and Probability, Springer |
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| ADDITIONAL NOTES | Pre-Requisite Study-Units: SOR1110, SOR2211 and SOR3110 | ||||||||
| STUDY-UNIT TYPE | Lecture | ||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Lino Sant |
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The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to study-units available during the academic year 2023/4. It may be subject to change in subsequent years. |
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