# Measure Theory by M Usman Hamid & Saima Akram

The main aim of this course is to develop a more satisfactory theory of integration to overcome above mentioned drawbacks by Muhammad Usman Hamid

The Riemann integral, dealt with in calculus courses, is well suited for computations but less suited for dealing with limit processes. In this course we will introduce the so called Lebesgue integral, which keeps the advantages of the Riemann integral and eliminates its drawbacks by Saima Akram

 Name Measure Theory Muhammad Usman Hamid & Saima Akram 127 pages PDF (see Software section for PDF Reader) 2.02 MB
• Algebras and Sigma-Algebras
• Measures, Outer Measures
• Lebesgue Measure
• Measurable sets and Lebesgue measure
• A non-measurable set
• Completeness and Regularity
• Functions and Integrals
• Measurable Functions
• Properties That Hold Almost Everywhere
• Lebesgue integration: the Lebesgue integral of a non-negative function
• The general Lebesgue integral;
• General measure and integration measure spaces
• The Integral
• Limit Theorems
• The Riemann Integral
• Measurable Functions Again
• Complex-Valued Functions, and
• Image Measures, Convergence
• Modes of Convergence
• Definition and Properties Signed measures
• Outer measure and measurability
• The extension theorem
• The Lebesgue Stieltjes integral
• Product measures

• msc/notes/measure-thoery-muhsa