Lawrence Craig Evans and Ronald F. Gariepy, Measure theory and fine properties of functions, 2nd revised ed., Textbooks in Mathematics, CRC Press, Boca Raton, FL, 2015, xi+309 pp., ISBN: 978-1-4822-4238-6/hbk. - ANISIU, Valeriu (Studia Universitatis Babeș-Bolyai Mathematica, 2015)
This is a new revised edition of a very successful book (published by CRC Pressin 1992) dealing with measure theory in Rn and some special properties of functions,usually omitted from books dealing with abstract measure theory, but which a workingmathematician analyst must to know. Among these special topics we mention: Vitali'sand Besicovitch's covering theorems, Hausdor measures and capacities (for classifyingclasses of negligible sets for various ne properties of functions), Rademacher'sTheorem on the a.e. dierentiability of Lipschitz functions (a topic of great actualinterest in connection with its extension to in nite dimensions), the area and coareaformulas (yielding change-of-variable rules for Lipschitz functions between Rn andRm), the Lebesgue-Besicovitch dierentiation theorem, the precise structure of BVand Sobolev functions, Alexandrov's theorem on a.e. twice differentiability of convexfunctions, Whithney's extension theorem with applications to approximation ofSobolev and BV functions, etc. The book is clearly written with complete proofs,including all technicalities. One assumes that the reader is familiar with Lebesguemeasure and abstract measure theory.