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On the measure of Cartesian product sets
Author:
Gerald Freilich
Journal:
Trans. Amer. Math. Soc. 69 (1950), 232-275
MSC:
Primary 27.2X
MathSciNet review:
0037893
Full-text PDF Free Access
References |
Similar Articles |
Additional Information
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A.
S. Besicovitch and P.
A. P. Moran, The measure of product and cylinder sets, J.
London Math. Soc. 20 (1945), 110–120. MR 0016448
(8,18f)
- [BF]
J. Bonnesen and W. Fenchel Theorie der konvexen Körper, Ergebnisse der Mathematik, vol. 3, part 1, 1934.
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C. Carathéodory Über das lineare Mass von Punktmengen--eine Verallgemeinerung des Längenbegriffs, Nachr. Ges. Wiss. Göttingen (1914) pp. 404-426.
- [F1]
Herbert
Federer, Coincidence functions and their
integrals, Trans. Amer. Math. Soc. 59 (1946), 441–466. MR 0015466
(7,422a), http://dx.doi.org/10.1090/S0002-9947-1946-0015466-0
- [F2]
Herbert
Federer, The (𝜙,𝑘) rectifiable
subsets of 𝑛-space, Trans. Amer.
Soc. 62 (1947),
114–192. MR 0022594
(9,231c), http://dx.doi.org/10.1090/S0002-9947-1947-0022594-3
- [F3]
Herbert
Federer, Dimension and measure, Trans. Amer. Math. Soc. 62 (1947), 536–547. MR 0023325
(9,339g), http://dx.doi.org/10.1090/S0002-9947-1947-0023325-3
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Felix
Hausdorff, Dimension und äußeres Maß, Math.
Ann. 79 (1918), no. 1-2, 157–179 (German). MR
1511917, http://dx.doi.org/10.1007/BF01457179
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Lynn
H. Loomis, Abstract congruence and the uniqueness of Haar
measure, Ann. of Math. (2) 46 (1945), 348–355.
MR
0011713 (6,205a)
- [MF]
H.
Federer and A.
P. Morse, Some properties of measurable
functions, Bull. Amer. Math. Soc. 49 (1943), 270–277. MR 0007916
(4,213d), http://dx.doi.org/10.1090/S0002-9904-1943-07896-2
- [MR]
Anthony
P. Morse and John
F. Randolph, Gillespie measure, Duke Math. J.
6 (1940), 408–419. MR 0001832
(1,304a)
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Hans
Rademacher, Über partielle und totale differenzierbarkeit von
Funktionen mehrerer Variabeln und über die Transformation der
Doppelintegrale, Math. Ann. 79 (1919), no. 4,
340–359 (German). MR
1511935, http://dx.doi.org/10.1007/BF01498415
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J.
F. Randolph, On generalizations of length and
area, Bull. Amer. Math. Soc.
42 (1936), no. 4,
268–274. MR
1563283, http://dx.doi.org/10.1090/S0002-9904-1936-06287-7
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S. Saks Theory of the integral, Warsaw, 1937.
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A. Weil L'intégration dans les groupes topologiques et ses applications, Actualités Scientifiques et Industrielles, vol. 869, Hermann, Paris, 1938.
- [BM]
- A. S. Besicovitch and P. A. P. Moran The measure of product and cylinder sets, J. London Math. Soc. vol. 20 (1945) pp.110-120. MR 0016448 (8:18f)
- [BF]
- J. Bonnesen and W. Fenchel Theorie der konvexen Körper, Ergebnisse der Mathematik, vol. 3, part 1, 1934.
- [C]
- C. Carathéodory Über das lineare Mass von Punktmengen--eine Verallgemeinerung des Längenbegriffs, Nachr. Ges. Wiss. Göttingen (1914) pp. 404-426.
- [F1]
- H. Federer Coincidence functions and their integrals, Trans. Amer. Math. Soc. vol. 59 (1946) pp. 441-466. MR 0015466 (7:422a)
- [F2]
- -The
rectifiable subsets of space, Trans. Amer. Math. Soc. vol. 62 (1947) pp. 114-192. MR 0022594 (9:231c)
- [F3]
- -Dimension and measure, Trans. Amer. Math. Soc. vol. 62 (1947) pp. 536-547. MR 0023325 (9:339g)
- [H]
- F. Hausdorff Dimension und aüsseres Mass, Math. Ann. vol. 79 (1918) pp. 157-179. MR 1511917
- [L]
- L. H. Loomis Abstract congruence and the uniqueness of Haar measure, Ann. of Math. vol. 46 (1945) pp. 348-355. MR 0011713 (6:205a)
- [MF]
- A. P. Morse and H. Federer Some properties of measurable functions, Bull. Amer. Math. Soc. vol. 49 (1943) pp. 270-277. MR 0007916 (4:213d)
- [MR]
- A. P. Morse and J. F. Randolph Gillespie measure, Duke Math. J. vol. 6 (1940) pp. 408-419. MR 0001832 (1:304a)
- [RAD]
- H. Rademacher Über partielle und totale Differenzierbarkeit. I, Math. Ann. vol. 79 (1919) pp. 340-359. MR 1511935
- [R]
- J. F. Randolph On generalizations of length and area, Bull. Amer. Math. Soc. vol. 42 (1936) pp. 268-274. MR 1563283
- [S]
- S. Saks Theory of the integral, Warsaw, 1937.
- [W]
- A. Weil L'intégration dans les groupes topologiques et ses applications, Actualités Scientifiques et Industrielles, vol. 869, Hermann, Paris, 1938.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1950-0037893-9
PII:
S 0002-9947(1950)0037893-9
Article copyright:
© Copyright 1950 American Mathematical Society
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