I did a swift check on Rudin's book on Principles of Mathematical Analysis:
The book covers in my opinion (and Rudin's as well:) a 1-year undergraduate course in analysis (at least that is what is taught in German universities) and a bit beyond (for example chapter 10).
All your topics (measure theory, integration, differentiation) are subject of one or more chapter in this very book. Although I haven't read this book, I think it would be a good choice to stick to the outline of this book by Rudin if you want to work with it - I am sure it is not a bad choice. I also could find some solution manuals on the internet, which might become in handy if you're doing a self-study course.
I would say the outcome of working through the book is a very solid knowledge on analysis, a good companion for advanced studies in mathematics.
bests
manpreet![Tuteehub forum best answer]()
Best Answer
3 years ago
I have following syllabus to study in Real Analysis Subject. I want to know, What are necessary topics that I have to cover as a prerequisite for below syllabus.
Actually I am unable to get direction as this subject is very big. Can someone help me in providing point wise preliminaries topics for below syllabus?
Below is syllabus -
**1. Measure Theory: Preliminaries, Exterior Measure, Measurable Sets and Lebesgue Measure, Measurable Functions.
2. Integration Theory: The Lebesgue Integral, basic properties and convergence theorems. The space L1L1 of integrable functions, Fubini’s theorem.
3. Differentiation and Integration: Differentiation of the integral, Good kernels and approximation to the identity, differentiation of functions.**
Already I am studying Rudin's book. Still I don't know how much it will help me in scoring.
Thanks in advance.