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This is a question on a self-study matter. Earlier, I stopped reading W. Rudin's book on "principles of mathematical analysis", at the chapter on Riemann integration. Now for certain other needs, I need to study Lebesgue integration; nothing too difficult; I would imagine the last chapter of this book would suffice without learning the whole difficult machinery as in Rudin's bigger book "Real and Complex Analysis". The purpose is to read a book on ergodic theory later.

Up to now I had read the book line by line, page by page, and right now I am on the chapter on sequences and series of functions. My question is, whether this topic is relevant to Lebesgue integration and if I can skip this. For the earlier chapters, I found that skipping something in between for a topic so basic as analysis is a bad idea and I would miss something. On the other hand, learning a chapter which on the surface has nothing to do with integration, gives a feeling of lack of motivation, and therefore there is less enthusiasm to study. If I can skip this chapter and the rest and go straight to the last chapter, I would perhaps be able to proceed faster, and with more interest.

So, please advice me from the viewpoint of more experienced people, whether I can safely skip the chapter on sequences and series without too much harm.

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    Sequences of functions are essential for **USING** Lebesgue integration, and sometimes even for defining Lebesgue integration (depending on the approach). Lebesgue integration to Riemann integration is like the real numbers to the rational numbers. You need the real numbers to appropriately handle situations when sequences and series of numbers arise, and in an analogous way, you need Lebesgue integration to appropriately handle situations when sequences and series of functions arise.2012-07-17

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You can skip on first reading, and go straight to the chapter on Lebesgue integration you are interested in. Then if and when you encounter something that involves sequences or series of functions which needs clarification, you can go back and read the relevant chapter piece by piece, or as a whole, depending on your interest. My guess is by that time you will develop a will to read this chapter on sequences or series of functions since you would have encountered many motivating reasons. On another, more general note, you should learn about sequences and series of functions sooner or later because their importance is not limited to the context of Lebesgue integration.

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    Can you explain why -1? I am not trolling. I spent some effort answering this question. If you have an argument to support the view that this answer is downright incorrect, please provide here, since it would serve the reader better than just a downvote.2012-06-09