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Can anyone provide references for Radon measures, Bounded variation functions space, and Lebesgue differentiation theorem for Radon Measures, Hausdorff dimensions?


Online references will be preferred but other references will also be welcomed!

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These should all be covered in any intro to measure theory and analysis book.

I learned all these from Folland's Real Analysis. In general, I would say that it's a good book. I would also say, however, that it suffers from its own linearity more than usual. By that, I mean that the proofs and concepts are so cumulatively presented that often, in order to appreciate a theorem or proof on page 250, say, you might need to understand all previous material. In fact, I suspect many proof chains can be traced all the way back to the beginning of the book.

Fortunately, radon measures, lebesgue differentiation, and bounded variation all occur near the beginning, and Hausdorff dimension is almost entirely self-contained. So I doubly recommend it to you.

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I agree, Folland's book is great. – Stefan Smith Mar 14 '12 at 23:35

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