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Название: Higher order Fourier analysis
Автор: Tao T.
This text presumes a graduate-level familiarity with basic real analysis and measure theory, such as is covered in [Ta2011], [Ta2010], particularly with regard to the "soft" or "qualitative" side of the subject.
The core of the text is Chapter 1, which comprise the main lecture material. The material in Chapter 2 is optional to these lectures, except for the ultrafilter material in Section 2.1 which would be needed to some extent in order to facilitate the ultralimit analysis in Chapter 1. However, it is possible to omit the portions of the text involving ultrafilters and still be able to cover most of the material (though from a narrower set of perspectives).