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Advanced analysis on the real line. (English) Zbl 0855.26001
Universitext. New York, NY: Springer. ix, 259 p. DM 68.00; S̎ 496.40; sFr 60.00 (1996).
This is a textbook destined for readers acquainted with elementary real analysis (including the theory of Lebesgue integration on the real line). In fact, the authors discuss a lot of subjects usually not included in introductory textbooks: approximate continuity, properties of Dini derivatives, the Denjoy-Young-Saks theorem both for Dini and approximate derivatives, Stieltjes integral, absolute continuity and rectifiability, Hausdorff measures, generalized Cantor sets, Hausdorff dimension, convergence in variation and in length, etc. The rich content is completed by a long list of references, by indicating at each theorem the sources referred to. Unfortunately, an unexperienced reader may be confused by some inaccuracies both in the definitions and in the proofs, as well as inconsistencies with respect to the presumed preliminary knowledge.
MSC:
26-01Textbooks (real functions)
28-01Textbooks (measure and integration)