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I am an economics student and want to study mathematics, variational analysis in particular, with measure approach but since I am ignorant of measure theory I decided to try this book but I still find it a bit difficult. What would you offer to a complete beginner?

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  • $\begingroup$ Tao authored two undergraduate level books:$\;(1)\;$Tao -- Analysis 1 (2006)$\;(2)\;$Tao -- Analysis 2 (2006), which presumably could be regarded as prerequisite knowledge. $\endgroup$
    – quasi
    Oct 10, 2017 at 17:30
  • $\begingroup$ Is real analysis always taught prior to measure theory? and is variational analysis taught at undergrad level at all? $\endgroup$
    – roglol
    Oct 10, 2017 at 17:41
  • $\begingroup$ Real Analysis usually includes Measure Theory. But undergraduate analysis is certainly a prerequisite to graduate-level analysis. $\endgroup$
    – quasi
    Oct 10, 2017 at 17:51
  • $\begingroup$ As for Variational Analysis, I would assume that it would normally be graduate-level material. $\endgroup$
    – quasi
    Oct 10, 2017 at 17:53
  • $\begingroup$ Is there a preface or introduction that states the prerequisites? $\endgroup$ Oct 10, 2017 at 20:44

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If you want to learn measure theory (and analysis in general), you should start at the undergraduate level. Lebesgue theory and measure theory aren't going to make sense if you aren't familiar with the standard tricks involved in analysis. Start with a book like Tao's undergrad analysis books and then move onto something like Rudin's Principles of Mathematical Analysis. Rudin's text is very terse, but universally considered as a standard text in the field. As for measure theory, I recommend Royden and Fitzpatrick's Real Analysis, 4th Edition.

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  • $\begingroup$ yeah it seems so complicated because all the mathematics i know is single variable calculus and in my country there is no university where I can study mathematics. $\endgroup$
    – roglol
    Oct 10, 2017 at 19:37

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