| Title:
|
О Лебеговой площади простых замкнутых поверхностей (Russian) |
| Title:
|
On the Lebesgue area of simple closed surfaces (English) |
| Author:
|
Král, Josef |
| Language:
|
Russian |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
12 |
| Issue:
|
1 |
| Year:
|
1962 |
| Pages:
|
44-68 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| MSC:
|
28.80 |
| idZBL:
|
Zbl 0111.25702 |
| idMR:
|
MR0147620 |
| DOI:
|
10.21136/CMJ.1962.100497 |
| . |
| Date available:
|
2008-06-09T13:13:16Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/100497 |
| . |
| Reference:
|
[1] П. С. Александров: Комбинаторная топология.Москва-Ленинград 1947. Zbl 1153.11318 |
| Reference:
|
[2] A. S. Besicovitch: On the definition and value of the area of a surface.Quart. J. Math. vol. 16 (1945), 86-102. Zbl 0063.00350, MR 0014415, 10.1093/qmath/os-16.1.86 |
| Reference:
|
[3] L. Cesari: Surface area.Princeton, New Jersey 1956. Zbl 0073.04101, MR 0074500 |
| Reference:
|
[4] E. De Giorgi: Su una teoria generale della misura $(r - 1)$-dimensionale in uno spazio ad r dimensioni.Ann. Mat. Рurа Appl. (4), 36 (1954), 191-213. Zbl 0055.28504, MR 0062214, 10.1007/BF02412838 |
| Reference:
|
[5] E. De Giorgi: Nuovi teoremi relativi alle misure $(r - 1)$-dimensionali in uno spazio ad r dimensioni.Ricerche di Mat. 4 (1955), 95 - 113. Zbl 0066.29903, MR 0074499 |
| Reference:
|
[6] M. R. Demers, H. Federer: On Lebesgue area II.Trans. Amer. Math. Soc. vol. 90 (1959), 499-522. Zbl 0086.04801, MR 0102586, 10.1090/S0002-9947-1959-0102586-4 |
| Reference:
|
[7] H. Federer: An addition theorem for Lebesgue area.Proc. Amer. Math. Soc. vol. 6 (1955), 911-914. Zbl 0067.28301, MR 0073681, 10.1090/S0002-9939-1955-0073681-5 |
| Reference:
|
[8] H. Federer: On Lebesgue area.Annals of Math. vol. 61 (1955), 289-353. Zbl 0065.04002, MR 0067178, 10.2307/1969917 |
| Reference:
|
[9] H. Federer: A note on the Gauss - Green theorem.Proc. Amer. Math. Soc. 9 (1958), 447 - 451. Zbl 0087.27302, MR 0095245, 10.1090/S0002-9939-1958-0095245-2 |
| Reference:
|
[10] W. H. Fleming: Functions with generalized gradient and generalized surfaces.Ann. Mat. Pura Appl. (4) vol. 54 (1957), 93-104. Zbl 0082.26701, MR 0095923, 10.1007/BF02415193 |
| Reference:
|
[11] W. H. Fleming: Functions whose partial derivatives are measures.Bull. Amer. Math. Soc. vol. 64 (1958), 364-366. Zbl 0092.05401, MR 0099404, 10.1090/S0002-9904-1958-10235-9 |
| Reference:
|
[12] И. Крал (J. Král): О лебеговой площади замкнутых поверхностей.Чех. мат. жур. 9 (84) 1959, 470-471. MR 0111822 |
| Reference:
|
[13] J. Král: Poznámka o množinách, jejichž charakteristická funkce má za parciální derivaci zobecněnou míru.Čas. pěst. mat. 86 (1961), 178-194. |
| Reference:
|
[14] K. Krickeberg: Distributionen, Funktionen beschränkter Variation und Lebesguescher Inhalt nichtparametrischer Flächen.Ann. Mat. Рurа Appl. (4) 54 (1957), 105 - 134. Zbl 0082.26702, MR 0095922, 10.1007/BF02415194 |
| Reference:
|
[15] J. Mařík: The surface integral.Чех. мат. жур. 6 (81), 1956, 522 - 558. MR 0089891 |
| Reference:
|
[16] J. Mařík: Poznámka o délce Jordanovy křivky.Čas. pěst. mat. 83 (1958), 91 - 96. |
| Reference:
|
[17] M. H. A. Newman: Elements of the topology of plane sets of points.Cambridge 1954. MR 0044820 |
| Reference:
|
[18] W. F. Osgood: A Jordan curve of positive area.Trans. Amer. Math. Soc. vol. 4 (1903), 107-112. MR 1500628, 10.1090/S0002-9947-1903-1500628-5 |
| Reference:
|
[19] Chr. Y. Раuс: Considérations sur les gradients généralisés de G. Fichera et E. De Giorgi.Ann. Mat. Рurа Appl. (4) vol. 40 (1955), 183-192. MR 0078421 |
| Reference:
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[20] Chr. Y. Раuс: Functions with generalized gradients in the theory of cell functions.Ann. Mat. Рurа Appl. (4) vol. 44 (1957), 135-152. MR 0095924 |
| Reference:
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[21] T. Radó: Über den Begriff der Riemannschen Fläche.Acta litt. ас sc. Szeged, 1925, 101 - 121. |
| Reference:
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[22] T. Radó: Two-dimensional concepts of bounded variation and absolute continuity.Duke Math. J. 14 (1947), 587-608. MR 0022593 |
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[23] T. Radó: Length and area.New York 1948. MR 0024511 |
| Reference:
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[24] P. Slepian: Theory of Lebesgue area of continuous maps of 2-manifolds into n-space.Annals of Math. vol. 68 (1958), 669-689. Zbl 0083.28203, MR 0098819, 10.2307/1970161 |
| Reference:
|
[25] А. Г. Вumушкин: О многомерных вариациях.Москва 1955. |
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[26] G. T. Whyburn: Analytic topology.1942. Zbl 0117.15804, MR 0007095 |
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[27] R. L. Wilder: A converse of the Jordan-Brower separation theorem in three dimensions.Trans. Amer. Math. Soc. vol. 32 (1930), 233-240. MR 1501556, 10.1090/S0002-9947-1930-1501556-8 |
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|
[28] W. H. Fleming: Functions whose partial derivatives are measures.Illinois J. of Math. vol. 4 (1960), 452-478. Zbl 0151.05402, MR 0130338, 10.1215/ijm/1255456061 |
| . |
