THEORY OF MEASURE AND INTEGRATION

Compulsory course 3 credits.

Theory + Exercises: 3 credits

I. Overview

Introduction to positive measures, Lebesgue measures on Rⁿ , Lebesgue integration and it basic properties.

II. Prerequisites : Analysis 1, Analysis 2 and Analysis 3.

III. Contents

Chapter 1 : Integral relative to positive measures: positive measures, measurable functions, integrable functions, convergence theorems of Lebesgue, Fatou’s lemma.

Chapter 2 : Regularity of positive Borel measures. Lebesgue’s measure. Theorem of Lusin. Theorem Vitali–Caratheodory. Positive Borel measures: Riez’s theorem (without proof).

Chapter 3 : Integration on product spaces: measure on product spaces, Fubini’s theorem., Formula of change variables..

References

[1] R.G. Bartle, The elements of integration, John Wiley and Son, New York, 1966.

[2] Duong Minh Duc, Theory of measure and integration. (Vietnamese) .

[3] W. Rudin, Real and complex analysis, . McGraw-Hill, New York 1970.