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Book Information:
Authors:
Joe Diestel and
Angela Spalsbury
Title:
The joys of Haar measure
Additional book information:
Graduate Studies in Mathematics, Vol. 150,
American Mathematical Society,
Providence, RI,
xiv+320 pp.,
ISBN 978-1-4704-0935-7,
US$65
N. H. Bingham and A. J. Ostaszewski, The Steinhaus theorem and regular variation: de Bruijn and after, Indag. Math. (N.S.) 24 (2013), no. 4, 679–692. MR 3124800, DOI 10.1016/j.indag.2013.05.002
Krzysztof Chris Ciesielski and Joseph Rosenblatt, Restricted continuity and a theorem of Luzin, Colloq. Math. 135 (2014), no. 2, 211–225. MR 3229417, DOI 10.4064/cm135-2-5
V. G. Drinfel′d, Finitely-additive measures on $S^{2}$ and $S^{3}$, invariant with respect to rotations, Funktsional. Anal. i Prilozhen. 18 (1984), no. 3, 77 (Russian). MR 757256
Lester Dubins, Morris W. Hirsch, and Jack Karush, Scissor congruence, Israel J. Math. 1 (1963), 239–247. MR 165424, DOI 10.1007/BF02759727
G. A. Edgar and J. M. Rosenblatt, Difference equations over locally compact abelian groups, Trans. Amer. Math. Soc. 253 (1979), 273–289. MR 536947, DOI 10.1090/S0002-9947-1979-0536947-9
Martin H. Ellis, Sweeping out under a collection of transformations, Math. Z. 165 (1979), no. 3, 213–221. MR 523122, DOI 10.1007/BF01437556
P. Erdős, Remarks on some problems in number theory, Math. Balkanica 4 (1974), 197–202. MR 429704
L. Grabowski, A. Máthé, and O. Pikhurko, Measurable circle squaring, arXiv:1501.06122v1, January 25, 2015.
Christopher Heil, Jayakumar Ramanathan, and Pankaj Topiwala, Linear independence of time-frequency translates, Proc. Amer. Math. Soc. 124 (1996), no. 9, 2787–2795. MR 1327018, DOI 10.1090/S0002-9939-96-03346-1
Paul D. Humke and Miklós Laczkovich, A visit to the Erdős problem, Proc. Amer. Math. Soc. 126 (1998), no. 3, 819–822. MR 1425126, DOI 10.1090/S0002-9939-98-04167-7
M. Laczkovich, Equidecomposability and discrepancy; a solution of Tarski’s circle-squaring problem, J. Reine Angew. Math. 404 (1990), 77–117. MR 1037431, DOI 10.1515/crll.1990.404.77
Peter A. Linnell and Michael J. Puls, Zero divisors and $L^p(G)$. II, New York J. Math. 7 (2001), 49–58. MR 1838472
G. A. Margulis, Some remarks on invariant means, Monatsh. Math. 90 (1980), no. 3, 233–235. MR 596890, DOI 10.1007/BF01295368
R. Daniel Mauldin (ed.), The Scottish Book, Birkhäuser, Boston, Mass., 1981. Mathematics from the Scottish Café; Including selected papers presented at the Scottish Book Conference held at North Texas State University, Denton, Tex., May 1979. MR 666400
A. J. Ostaszewski, Beyond Lebesgue and Baire III: Steinhaus’ theorem and its descendants, Topology Appl. 160 (2013), no. 10, 1144–1154. MR 3056005, DOI 10.1016/j.topol.2013.04.005
John C. Oxtoby, Measure and category. A survey of the analogies between topological and measure spaces, Graduate Texts in Mathematics, Vol. 2, Springer-Verlag, New York-Berlin, 1971. MR 0393403
Sophie Piccard, Sur des ensembles parfaits, Mém. Univ. Neuchâtel, vol. 16, Université de Neuchâtel, Secrétariat de l’Université, Neuchâtel, 1942 (French). MR 0008835
Michael J. Puls, Zero divisors and $L^p(G)$, Proc. Amer. Math. Soc. 126 (1998), no. 3, 721–728. MR 1415362, DOI 10.1090/S0002-9939-98-04025-8
Joseph Rosenblatt, Linear independence of translations, Int. J. Pure Appl. Math. 45 (2008), no. 3, 463–473. MR 2418032
Joseph Rosenblatt, Linear independence of translations, J. Austral. Math. Soc. Ser. A 59 (1995), no. 1, 131–133. MR 1336456
Dennis Sullivan, For $n>3$ there is only one finitely additive rotationally invariant measure on the $n$-sphere defined on all Lebesgue measurable subsets, Bull. Amer. Math. Soc. (N.S.) 4 (1981), no. 1, 121–123. MR 590825, DOI 10.1090/S0273-0979-1981-14880-1
H. Steinhaus,Sur les distances des points dans les ensembles de mesure positive, Fundamenta Math 1 (1920), 93-104.
A. Tarski, Problème 38, Fundamenta Math 7 (1925), 381.
Stan Wagon, The Banach-Tarski paradox, Encyclopedia of Mathematics and its Applications, vol. 24, Cambridge University Press, Cambridge, 1985. With a foreword by Jan Mycielski. MR 803509, DOI 10.1017/CBO9780511609596
References
- N. H. Bingham and A. J. Ostaszewski, The Steinhaus theorem and regular variation: de Bruijn and after, Indag. Math. (N.S.) 24 (2013), no. 4, 679–692. MR 3124800, DOI 10.1016/j.indag.2013.05.002
- Krzysztof Chris Ciesielski and Joseph Rosenblatt, Restricted continuity and a theorem of Luzin, Colloq. Math. 135 (2014), no. 2, 211–225. MR 3229417, DOI 10.4064/cm135-2-5
- V. G. Drinfel′d, Finitely-additive measures on $S^{2}$ and $S^{3}$, invariant with respect to rotations, Funktsional. Anal. i Prilozhen. 18 (1984), no. 3, 77 (Russian). MR 757256 (86a:28021)
- Lester Dubins, Morris W. Hirsch, and Jack Karush, Scissor congruence, Israel J. Math. 1 (1963), 239–247. MR 0165424 (29 \#2706)
- G. A. Edgar and J. M. Rosenblatt, Difference equations over locally compact abelian groups, Trans. Amer. Math. Soc. 253 (1979), 273–289. MR 536947 (80i:39001), DOI 10.2307/1998197
- Martin H. Ellis, Sweeping out under a collection of transformations, Math. Z. 165 (1979), no. 3, 213–221. MR 523122 (80d:28035), DOI 10.1007/BF01437556
- P. Erdős, Remarks on some problems in number theory, Math. Balkanica 4 (1974), 197–202. Papers presented at the Fifth Balkan Mathematical Congress (Belgrade, 1974). MR 0429704 (55 \#2715)
- L. Grabowski, A. Máthé, and O. Pikhurko, Measurable circle squaring, arXiv:1501.06122v1, January 25, 2015.
- Christopher Heil, Jayakumar Ramanathan, and Pankaj Topiwala, Linear independence of time-frequency translates, Proc. Amer. Math. Soc. 124 (1996), no. 9, 2787–2795. MR 1327018 (96k:42039), DOI 10.1090/S0002-9939-96-03346-1
- Paul D. Humke and Miklós Laczkovich, A visit to the Erdős problem, Proc. Amer. Math. Soc. 126 (1998), no. 3, 819–822. MR 1425126 (98e:28003), DOI 10.1090/S0002-9939-98-04167-7
- M. Laczkovich, Equidecomposability and discrepancy; a solution of Tarski’s circle-squaring problem, J. Reine Angew. Math. 404 (1990), 77–117. MR 1037431 (91b:51034), DOI 10.1515/crll.1990.404.77
- Peter A. Linnell and Michael J. Puls, Zero divisors and $L^p(G)$. II, New York J. Math. 7 (2001), 49–58 (electronic). MR 1838472 (2002d:43003)
- G. A. Margulis, Some remarks on invariant means, Monatsh. Math. 90 (1980), no. 3, 233–235. MR 596890 (82b:28034), DOI 10.1007/BF01295368
- R. Daniel Mauldin (ed.), The Scottish Book, Birkhäuser, Boston, Mass., 1981. Mathematics from the Scottish Café; Including selected papers presented at the Scottish Book Conference held at North Texas State University, Denton, Tex., May 1979. MR 666400 (84m:00015)
- A. J. Ostaszewski, Beyond Lebesgue and Baire III: Steinhaus’ theorem and its descendants, Topology Appl. 160 (2013), no. 10, 1144–1154. MR 3056005, DOI 10.1016/j.topol.2013.04.005
- John C. Oxtoby, Measure and category. A survey of the analogies between topological and measure spaces, Springer-Verlag, New York-Berlin, 1971. Graduate Texts in Mathematics, Vol. 2. MR 0393403 (52 \#14213)
- Sophie Piccard, Sur des ensembles parfaits, Mém. Univ. Neuchâtel, vol. 16, Secrétariat de l’Université, Neuchâtel, 1942 (French). MR 0008835 (5,61n)
- Michael J. Puls, Zero divisors and $L^p(G)$, Proc. Amer. Math. Soc. 126 (1998), no. 3, 721–728. MR 1415362 (98k:43001), DOI 10.1090/S0002-9939-98-04025-8
- Joseph Rosenblatt, Linear independence of translations, Int. J. Pure Appl. Math. 45 (2008), no. 3, 463–473. MR 2418032 (2009e:43008)
- Joseph Rosenblatt, Linear independence of translations, J. Austral. Math. Soc. Ser. A 59 (1995), no. 1, 131–133. MR 1336456 (96f:42009)
- Dennis Sullivan, For $n>3$ there is only one finitely additive rotationally invariant measure on the $n$-sphere defined on all Lebesgue measurable subsets, Bull. Amer. Math. Soc. (N.S.) 4 (1981), no. 1, 121–123. MR 590825 (82b:28035), DOI 10.1090/S0273-0979-1981-14880-1
- H. Steinhaus,Sur les distances des points dans les ensembles de mesure positive, Fundamenta Math 1 (1920), 93-104.
- A. Tarski, Problème 38, Fundamenta Math 7 (1925), 381.
- Stan Wagon, The Banach-Tarski paradox, Encyclopedia of Mathematics and its Applications, vol. 24, Cambridge University Press, Cambridge, 1985. With a foreword by Jan Mycielski. MR 803509 (87e:04007), DOI 10.1017/CBO9780511609596
Review Information:
Reviewer:
Joseph Rosenblatt
Affiliation:
Indiana University–Purdue University Indianapolis
Email:
joserose@iupui.edu
Journal:
Bull. Amer. Math. Soc.
52 (2015), 733-738
DOI:
https://doi.org/10.1090/bull/1499
Published electronically:
May 13, 2015
Review copyright:
© Copyright 2015
American Mathematical Society
