An Introduction to Measure and Integration SECOND EDITION , Inder K. Rana

  An Introduction to Measure and   Integration SECOND EDITION , Inder K. Rana 

    This text presents a motivated introduction to the theory of measure and integration.Starting with an historical introduction to the notion of integral and a preview of the Riemannintegral, the reader is motivated for the need to study the Lebesgue measure and Lebesgue integral.The abstract integration theory is developed via measure. Other basic topics discussed in the textare Fubini's Theorem, Lp-spaces, Radon-Nikodym Theorem, change of variables formulas, signedand complex measures.

Topics of this book divided in 10 chapters.  they are:

Chapter 1.Riemann integration
Chapter 2.Recipes for extending the Riemann integral
Chapter 3.General extension theory 
Chapter 4.The Lebesgue measure on R and its properties
Chapter 5.Integration
Chapter 6.Fundamental theorem of calculus for the Lebesgue integral
Chapter 7.Measure and integration on product spaces
Chapter 8.Modes of convergence and LP spaces
Chapter 9.The Radon-Nikodym theorem and its applications
Chapter 10.Signed measures and complex measures

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