Essentials in Analysis and Probability (U03864)

? Credit Points : 10 ? SCQF Level : 10 ? Acronym : MAT-4-EAP

Random events, sigma-algebras, monotone classes.
Measurable spaces, random variables - measurable functions.
Measures, probability measures, signed measures.
Borel sets in R^d, Lebesgue measure.
Sequences of events and random variables, Borel-Cantelli lemma.
Distributions of random variables. Independence of random variables.
Integral of measurable functions - mathematical expectation,.
Moments of random variables, L_p spaces.
Convergence concepts of measurable functions.
Limit theorems for integrals.
Week and strong laws of large numbers.
Completeness of L_p spaces.
Conditional expectation and conditional distribution of random variables.
Fubini's theorem.

Entry Requirements

? Pre-requisites : MAT-3-CVD, MAT-3-PAA

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Honours), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 4th year

? Delivery Period : Semester 1 (Blocks 1-2)

? Contact Teaching Time : 2 hour(s) per week for 11 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
20/09/2007	12:10	13:00	Lecture Room 5327, JCMB	KB

All of the following classes

Type	Day	Start	End	Area
Lecture	Monday	12:10	13:00	KB
Lecture	Thursday	12:10	13:00	KB

Summary of Intended Learning Outcomes

1. To provide the students with the basic notions and results from measure theory and integration, motivating them by fundamental concepts of probability theory.
2. To prepare a firm ground for further studies in analysis, in modern probability theory and in their applications.