To introduce the concepts of measure and integral with respect to a measure, to show their basic properties, and to provide a basis for further studies in Mathematical Analysis, Probability Measure Theory and Dynamical Systems. To construct Lebesgue's measure and learn the theory of Lebesgue integrals on real line.
INTENDED LEARNING OUTCOMES
Students will be able to
- generalize the idea of length of an interval
- Understand the length of a non-discrete set
- Class of measurable functions
- More general theory of integrals
- Convergence of sequences of measurable functions
- Lebesgue measure: introduction, outer measure.
- Measurable sets and Lebesgue measure.
- A non-measurable set.
- Measurable functions.
- The Lebesgue integral of a non-negative function.
- The general Lebesgue integral, general measure and integration measure spaces.
- Measurable functions, integration.
- General convergence theorems.
- Royden, H.L. and Fitzpatrick P.M, Real Analysis 4th ed.(NY:Collier Macmillan Co, 2017.)
- Philip E.R. An introduction to Analysis and Integration Theory. 1st ed.(USA:
- Bartle R.G, The Elements of Integration and Lebesgue Measure, 1st Ed.(Wiley-Interscience. 1995)
- Barra G. De. Measure Theory and Integration. 1st ed.( Ellis, Harwood Ltd, 1981. )
RESEARCH PROJECT /PRACTICALS/LABS/ASSIGNMENTS
The projects assigned in this course follow a new approch to theory of integration.
- Problem solving technique for measurable sets.
- Problems related to measurable functions and their properties.
- Different types of convergences of sequence of functions.
- Applications of convergence theorems for Lebesgue integrals.
Sessional: 20 (Presentation / Assignment 10, Attendance 05, Quiz 05)
Mid-Term Exam: 30
Final-Term Exam: 50
Key Dates and Time of Class Meeting
Wednesday 11:00 am-12:30 pm
Thursday 09:30 am-11:00 am
Commencement of Classes January 13, 2020
Mid Term Examination March 09-13, 2020
Final Term Examination May 04-08, 2020
Declaration of Result May 19, 2020