Sur l'intégration des fonctions discontinues
Annales scientifiques de l'École Normale Supérieure, Série 3, Tome 27 (1910), pp. 361-450. 
@article{ASENS_1910_3_27__361_0,
     author = {Lebesgue, Henri},
     title = {Sur l'int\'egration des fonctions discontinues},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {361--450},
     publisher = {Elsevier},
     volume = {3e s{\'e}rie, 27},
     year = {1910},
     doi = {10.24033/asens.624},
     language = {fr},
     url = {https://www.numdam.org/articles/10.24033/asens.624/}
}
TY  - JOUR
AU  - Lebesgue, Henri
TI  - Sur l'intégration des fonctions discontinues
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 1910
SP  - 361
EP  - 450
VL  - 27
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.24033/asens.624/
DO  - 10.24033/asens.624
LA  - fr
ID  - ASENS_1910_3_27__361_0
ER  - 
%0 Journal Article
%A Lebesgue, Henri
%T Sur l'intégration des fonctions discontinues
%J Annales scientifiques de l'École Normale Supérieure
%D 1910
%P 361-450
%V 27
%I Elsevier
%U https://www.numdam.org/articles/10.24033/asens.624/
%R 10.24033/asens.624
%G fr
%F ASENS_1910_3_27__361_0
Lebesgue, Henri. Sur l'intégration des fonctions discontinues. Annales scientifiques de l'École Normale Supérieure, Série 3, Tome 27 (1910), pp. 361-450. doi : 10.24033/asens.624. https://www.numdam.org/articles/10.24033/asens.624/
  • Lučić, Danka; Pasqualetto, Enrico The metric-valued Lebesgue differentiation theorem in measure spaces and its applications, Advances in Operator Theory, Volume 8 (2023) no. 2 | DOI:10.1007/s43036-023-00258-w
  • Beneduci, Roberto; Gentile, Tommaso Fuzzy observables and the universal family of fuzzy events, Fuzzy Sets and Systems, Volume 444 (2022), p. 206 | DOI:10.1016/j.fss.2022.03.008
  • Benci, Vieri An Improved Setting for Generalized Functions: Fine Ultrafunctions, Milan Journal of Mathematics, Volume 90 (2022) no. 2, p. 575 | DOI:10.1007/s00032-022-00359-w
  • Bru, Bernard; Eid, Salah Analysis or Probability? Eight Letters Between Børge Jessen and Paul Lévy, The Splendors and Miseries of Martingales (2022), p. 337 | DOI:10.1007/978-3-031-05988-9_15
  • Eid, Salah The Dawn of Martingale Convergence: Jessen’s Theorem and Lévy’s Lemma, The Splendors and Miseries of Martingales (2022), p. 67 | DOI:10.1007/978-3-031-05988-9_4
  • Brudnyi, Alexander; Brudnyi, Yuri Multivariate bounded variation functions of Jordan–Wiener type, Journal of Approximation Theory, Volume 251 (2020), p. 105346 | DOI:10.1016/j.jat.2019.105346
  • Ambartsoumian, G; Latifi Jebelli, M J The V-line transform with some generalizations and cone differentiation, Inverse Problems, Volume 35 (2019) no. 3, p. 034003 | DOI:10.1088/1361-6420/aafcf3
  • Becker, Simon; Hartmann, Carsten Infinite-dimensional bilinear and stochastic balanced truncation with explicit error bounds, Mathematics of Control, Signals, and Systems, Volume 31 (2019) no. 2, p. 1 | DOI:10.1007/s00498-019-0234-8
  • Busemann, Herbert; Feller, Willy Regularity Properties of a Certain Class of Surfaces, Selected Works II (2018), p. 271 | DOI:10.1007/978-3-319-65624-3_19
  • Sawano, Yoshihiro Elementary Facts on Harmonic Analysis, Theory of Besov Spaces, Volume 56 (2018), p. 1 | DOI:10.1007/978-981-13-0836-9_1
  • Nies, André Lowness, Randomness, and Computable Analysis, Computability and Complexity, Volume 10010 (2017), p. 738 | DOI:10.1007/978-3-319-50062-1_42
  • Filipczak, Małgorzata; Terepeta, Małgorzata; Wilczyński, Władysław Density, ψ-density and continuity, Mathematica Slovaca, Volume 67 (2017) no. 6, p. 1525 | DOI:10.1515/ms-2017-0067
  • Charatonik, Włodzimierz; Insall, Matt Measures on hyperspaces, Proceedings of the American Mathematical Society, Volume 144 (2016) no. 11, p. 4753 | DOI:10.1090/proc/13215
  • N. Sá, L. F.; R. Amigo, R. C.; Novotny, A. A.; N. Silva, E. C. Topological derivatives applied to fluid flow channel design optimization problems, Structural and Multidisciplinary Optimization, Volume 54 (2016) no. 2, p. 249 | DOI:10.1007/s00158-016-1399-0
  • MIYABE, KENSHI; NIES, ANDRÉ; ZHANG, JING USING ALMOST-EVERYWHERE THEOREMS FROM ANALYSIS TO STUDY RANDOMNESS, The Bulletin of Symbolic Logic, Volume 22 (2016) no. 3, p. 305 | DOI:10.1017/bsl.2016.10
  • Delfour, Michel C. Metric Spaces of Shapes and Geometries Constructed from Set Parametrized Functions, New Trends in Shape Optimization, Volume 166 (2015), p. 57 | DOI:10.1007/978-3-319-17563-8_4
  • Bessa, Mário; Carvalho, Maria; Rodrigues, Alexandre Generic area-preserving reversible diffeomorphisms, Nonlinearity, Volume 28 (2015) no. 6, p. 1695 | DOI:10.1088/0951-7715/28/6/1695
  • Mawhin, Jean The Cours d’Analyse Infinitésimale of Charles-Jean de La Vallée Poussin: From Innovation to Tradition, Jahresbericht der Deutschen Mathematiker-Vereinigung, Volume 116 (2014) no. 4, p. 243 | DOI:10.1365/s13291-014-0100-z
  • Bienvenu, Laurent; Hölzl, Rupert; Miller, Joseph S.; Nies, André Denjoy, Demuth and density, Journal of Mathematical Logic, Volume 14 (2014) no. 01, p. 1450004 | DOI:10.1142/s0219061314500044
  • Bibliography, Mathematical Foundations of Image Processing and Analysis 1 (2014), p. 309 | DOI:10.1002/9781118625705.biblio
  • Bibliography, Mathematical Foundations of Image Processing and Analysis 2 (2014), p. 349 | DOI:10.1002/9781118984574.biblio
  • Maurey, Bernard; Tacchi, Jean-Pierre Sur le théorème de recouvrement de Vitali, Archive for History of Exact Sciences, Volume 67 (2013) no. 1, p. 81 | DOI:10.1007/s00407-012-0109-6
  • Berezhnoj, Evgenii I. Admissible Differential Bases in Banach Spaces, International Journal of Mathematics and Mathematical Sciences, Volume 2013 (2013), p. 1 | DOI:10.1155/2013/748645
  • Miyabe, Kenshi Characterization of Kurtz Randomness by a Differentiation Theorem, Theory of Computing Systems, Volume 52 (2013) no. 1, p. 113 | DOI:10.1007/s00224-012-9422-3
  • Borgato, Maria Teresa Giuseppe Vitali: Real and Complex Analysis and Differential Geometry, Mathematicians in Bologna 1861–1960 (2012), p. 31 | DOI:10.1007/978-3-0348-0227-7_2
  • Siegmund-Schultze, Reinhard Sets versus trial sequences, Hausdorff versus von Mises: “Pure” mathematics prevails in the foundations of probability around 1920, Historia Mathematica, Volume 37 (2010) no. 2, p. 204 | DOI:10.1016/j.hm.2009.11.007
  • Inhalte und Maße, Reelle Zahlen (2008), p. 185 | DOI:10.1007/978-3-540-79376-2_9
  • Inhalte und Maße, Reelle Zahlen (2007), p. 185 | DOI:10.1007/978-3-540-45388-8_6
  • Werner, Strauss; Nikolaos, D. Macheras; Kazimierz, Musiat Liftings, Handbook of Measure Theory (2002), p. 1131 | DOI:10.1016/b978-044450263-6/50029-4
  • Integration, Real Analysis and Probability (2002), p. 114 | DOI:10.1017/cbo9780511755347.005
  • Lp Spaces; Introduction to Functional Analysis, Real Analysis and Probability (2002), p. 152 | DOI:10.1017/cbo9780511755347.006
  • Measure, Topology, and Differentiation, Real Analysis and Probability (2002), p. 222 | DOI:10.1017/cbo9780511755347.008
  • Бережной, Евгений Иванович; Berezhnoi, Evgenii Ivanovich; Новиков, Алексей Валерьевич; Novikov, Alexei Valer'evich О проблеме окаймления из теории дифференцирования интегралов, Известия Российской академии наук. Серия математическая, Volume 66 (2002) no. 4, p. 3 | DOI:10.4213/im393
  • Бережной, Евгений Иванович; Berezhnoi, Evgenii Ivanovich; Перфильев, Алексей Анатольевич; Perfil'ev, Aleksei Anatol'evich Различение симметричных пространств и L∞ с помощью дифференциального базиса, Математические заметки, Volume 69 (2001) no. 4, p. 515 | DOI:10.4213/mzm520
  • БЕРЕжНОИ, Е. И. О ДИФФЕРЕНцИРОВАНИИ ИНтЕгРАлОВ От ФУНкцИ И Иж сИММЕтРИЧНых пРОс тРАНстВ ДИФФЕРЕНцИАльНыМИ Б АжИсАМИ, Analysis Mathematica, Volume 22 (1996) no. 4, p. 267 | DOI:10.1007/bf01904787
  • Стоколос, Александр М; Stokolos, Alexander M О дифференцировании интегралов базисами, не обладающими свойством плотности, Математический сборник, Volume 187 (1996) no. 7, p. 113 | DOI:10.4213/sm148
  • Berezhnoi, E. I. Differential properties of bases and halo problem for rearrangement-invariant spaces, Siberian Mathematical Journal, Volume 36 (1995) no. 6, p. 1065 | DOI:10.1007/bf02106832
  • Pier, Jean-Paul Intégration et mesure 1900–1950, Development of Mathematics 1900–1950 (1994), p. 517 | DOI:10.1007/978-3-0348-9114-1_12
  • Stokolos, A. M. On the strong differentiation of integrals of functions from hölder classes, Mathematical Notes, Volume 55 (1994) no. 1, p. 57 | DOI:10.1007/bf02110767
  • Hazewinkel, M. V, Encyclopaedia of Mathematics (1993), p. 357 | DOI:10.1007/978-94-015-1233-6_4
  • Luxemburg, Wilhelmus A. J. The Stieltjes Integral, the Concept that Transformed Analysis, Œuvres Complètes Collected Papers (1993), p. 57 | DOI:10.1007/978-3-642-61229-9_4
  • Taylor, Angus E. A study of Maurice Fr�chet: III. Fr�chet as analyst, 1909?1930, Archive for History of Exact Sciences, Volume 37 (1987) no. 1, p. 25 | DOI:10.1007/bf00412329
  • de Guzmán, Miguel The Evolution of Some Ideas in the Theory of Differentiation of Integrals, Aspects of Mathematics and its Applications, Volume 34 (1986), p. 377 | DOI:10.1016/s0924-6509(09)70267-3
  • Gray, J. D. The shaping of the riesz representation theorem: A chapter in the history of analysis, Archive for History of Exact Sciences, Volume 31 (1984) no. 2, p. 127 | DOI:10.1007/bf00348293
  • Stokolos, A. M. An inequality for equimeasurable rearrangements and its application in the theory of differentiation of integrals, Analysis Mathematica, Volume 9 (1983) no. 2, p. 133 | DOI:10.1007/bf01982009
  • Johnson, Dale M. The problem of the invariance of dimension in the growth of modern topology, part II, Archive for History of Exact Sciences, Volume 25 (1981) no. 2-3, p. 85 | DOI:10.1007/bf02116242
  • SELECTED BIBLIOGRAPHY, Measure and Integral (1978), p. 549 | DOI:10.1016/b978-0-12-378550-3.50023-2
  • Henstock, Ralph Integration by parts, Aequationes Mathematicae, Volume 9 (1973) no. 1, p. 1 | DOI:10.1007/bf01838184
  • Bongiorno, Benedetto Sulla sommabilità delle derivate di una funzione arbitraria d’insieme, Rendiconti del Circolo Matematico di Palermo, Volume 21 (1972) no. 1-2, p. 183 | DOI:10.1007/bf02844242
  • Wright, Harvel; Snyder, W. S. On the differentiability of arbitrary real-valued set functions. II., Transactions of the American Mathematical Society, Volume 161 (1971) no. 0, p. 111 | DOI:10.1090/s0002-9947-1971-0281864-8
  • CONCLUSION, Classical and Modern Integration Theories (1970), p. 178 | DOI:10.1016/b978-0-12-552550-3.50018-7
  • Wright, Harvel; Snyder, W. S. On the differentiability of arbitrary real-valued set functions. I., Transactions of the American Mathematical Society, Volume 145 (1969) no. 0, p. 439 | DOI:10.1090/s0002-9947-1969-0251185-9
  • Rosenthal, Arthur What are Set Functions?, The American Mathematical Monthly, Volume 55 (1948) no. 1, p. 14 | DOI:10.1080/00029890.1948.11991896
  • Busemann, H.; Feller, W. Regularity properties of a certain class of surfaces, Bulletin of the American Mathematical Society, Volume 51 (1945) no. 8, p. 583 | DOI:10.1090/s0002-9904-1945-08403-1
  • Henri Lebesgue, 1875 - 1941, Obituary Notices of Fellows of the Royal Society, Volume 4 (1944) no. 13, p. 483 | DOI:10.1098/rsbm.1944.0001
  • Jessen, B. The theory of integration in a space of an infinite number of dimensions, Acta Mathematica, Volume 63 (1934) no. 0, p. 249 | DOI:10.1007/bf02547355
  • Gergen, J. J. Convergence criteria for double Fourier series, Transactions of the American Mathematical Society, Volume 35 (1933) no. 1, p. 29 | DOI:10.1090/s0002-9947-1933-1501671-1
  • Boks, T. J. Sur les rapports entre les méthodes d’intégration deRiemann et deLebesgue, Rendiconti del Circolo Matematico di Palermo, Volume 45 (1921) no. 1, p. 211 | DOI:10.1007/bf03018141
  • Knopp, Konrad Bemerkungen zur Struktur einer linearen perfekten nirgends dichten Punktmenge, Mathematische Annalen, Volume 77 (1916) no. 3, p. 438 | DOI:10.1007/bf01475872
  • Küstermann, Walter Funktionen von beschränkter Schwankung in zwei reellen Veränderlichen, Mathematische Annalen, Volume 77 (1916) no. 4, p. 474 | DOI:10.1007/bf01456963
  • Rademacher, Hans Eineindeutige Abbildungen und Meßbarkeit, Monatshefte für Mathematik und Physik, Volume 27 (1916) no. 1, p. 183 | DOI:10.1007/bf01726741
  • Bauer, Hans Der Perronsche Integralbegriff und seine Beziehung zum Lebesgueschen, Monatshefte für Mathematik und Physik, Volume 26 (1915) no. 1, p. 153 | DOI:10.1007/bf01999447
  • Fubini, Guido; Tonelli, Leonida Sulla derivata seconda mista di un integrale doppio, Rendiconti del Circolo Matematico di Palermo, Volume 40 (1915) no. 1, p. 295 | DOI:10.1007/bf03014857
  • Oseen, C. W. Über einen satz von green und über die definitionen von rot und div, Rendiconti del Circolo Matematico di Palermo, Volume 38 (1914) no. 1, p. 167 | DOI:10.1007/bf03015189

Cité par 64 documents. Sources : Crossref