Book Review
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MathSciNet review:
1568174
Full text of review:
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This review is available free of charge.
Book Information:
Author:
L.C. Evans and R. Gariepy
Title:
Measure theory and fine properties of functions
Additional book information:
CRC Press, Boca Raton, Ann Arbor, and London, 1992, viii + 268 pp., US$59.95. ISBN 0-8493-7157-0.
Ennio De Giorgi, Su una teoria generale della misura $(r-1)$-dimensionale in uno spazio ad $r$ dimensioni, Ann. Mat. Pura Appl. (4) 36 (1954), 191–213 (Italian). MR 62214, DOI 10.1007/BF02412838
Ennio De Giorgi, Frontiere orientate di misura minima, Editrice Tecnico Scientifica, Pisa, 1961 (Italian). Seminario di Matematica della Scuola Normale Superiore di Pisa, 1960-61. MR 0179651
Herbert Federer, The Gauss-Green theorem, Trans. Amer. Math. Soc. 58 (1945), 44–76. MR 13786, DOI 10.1090/S0002-9947-1945-0013786-6
Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York, Inc., New York, 1969. MR 0257325
Wendell H. Fleming and Raymond Rishel, An integral formula for total gradient variation, Arch. Math. (Basel) 11 (1960), 218–222. MR 114892, DOI 10.1007/BF01236935
Herbert Federer and William P. Ziemer, The Lebesgue set of a function whose distribution derivatives are $p$-th power summable, Indiana Univ. Math. J. 22 (1972/73), 139–158. MR 435361, DOI 10.1512/iumj.1972.22.22013
Enrico Giusti, Minimal surfaces and functions of bounded variation, Monographs in Mathematics, vol. 80, Birkhäuser Verlag, Basel, 1984. MR 775682, DOI 10.1007/978-1-4684-9486-0
Leon Simon, Lectures on geometric measure theory, Proceedings of the Centre for Mathematical Analysis, Australian National University, vol. 3, Australian National University, Centre for Mathematical Analysis, Canberra, 1983. MR 756417
[V] A.I. Vol'pert, The spaces BV and quasi-linear equations, Mat. Sb. 73 (1967), 255-302 (Russian); English transl., Math. USSR Sb. 2 (1967), 225-267.
William P. Ziemer, Weakly differentiable functions, Graduate Texts in Mathematics, vol. 120, Springer-Verlag, New York, 1989. Sobolev spaces and functions of bounded variation. MR 1014685, DOI 10.1007/978-1-4612-1015-3
- [DG1]
- E. DeGiorgi, Su una teoria generale misura
-dimensionale in uno spazio ad r dimensioni, Ann. Mat. Pura Appl. (4) 36 (1954), 191-213. MR 0062214 (15:945d)
- [DG2]
- -, Frontiere orientate di misura minima, Sem. Mat. Scuola Norm. Sup. Pisa, 1960-61, Editrice Tecnico Scientifica, Pisa, 1961. MR 0179651 (31:3897)
- [F1]
- H. Federer, The Gauss-Green theorem, Trans. Amer. Math. Soc. 9 (1945), 44-76. MR 0013786 (7:199b)
- [F2]
- -, Geometric measure theory, Springer-Verlag, Berlin, Heidelberg, and New York, 1969. MR 0257325 (41:1976)
- [F-R]
- W. Fleming and R. Rishel, An integral formula for the total gradient variation, Arch. Math. 11 (1960), 218-222. MR 0114892 (22:5710)
- [F-Z]
- H. Federer and W. Ziemer, The Lebesgue set of a function whose distribution derivatives are p-th power summable, Indiana Univ. Math. J. 22 (1972), 139-158. MR 0435361 (55:8321)
- [G]
- E. Giusti, Minimal surfaces and functions of bounded variation, Birkhäuser, Boston, 1984. MR 775682 (87a:58041)
- [S]
- L. Simon, Lectures on geometric measure theory, Centre for Mathematical Analysis, Australian National Univ., Canberra, 1984. MR 756417 (87a:49001)
- [V]
- A.I. Vol'pert, The spaces BV and quasi-linear equations, Mat. Sb. 73 (1967), 255-302 (Russian); English transl., Math. USSR Sb. 2 (1967), 225-267.
- [Z]
- W. Ziemer, Weakly differentiable functions, Springer-Verlag, Berlin and New York, 1989. MR 1014685 (91e:46046)
Review Information:
Reviewer:
Robert Hardt
Journal:
Bull. Amer. Math. Soc.
32 (1995), 285-288
DOI:
https://doi.org/10.1090/S0273-0979-1995-00579-3
