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Course Queries Syllabus Queries 2 years ago
Posted on 16 Aug 2022, this text provides information on Syllabus Queries related to Course Queries. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.
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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.
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.
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