Mémoire sur les fonctions discontinues
Annales scientifiques de l'École Normale Supérieure, Série 2, Tome 4 (1875), pp. 57-112. 
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     author = {Darboux, Gaston},
     title = {M\'emoire sur les fonctions discontinues},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {57--112},
     publisher = {Elsevier},
     volume = {2e s{\'e}rie, 4},
     year = {1875},
     doi = {10.24033/asens.122},
     language = {fr},
     url = {https://www.numdam.org/articles/10.24033/asens.122/}
}
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Darboux, Gaston. Mémoire sur les fonctions discontinues. Annales scientifiques de l'École Normale Supérieure, Série 2, Tome 4 (1875), pp. 57-112. doi : 10.24033/asens.122. https://www.numdam.org/articles/10.24033/asens.122/
  • Sanders, Sam Sometimes tame, sometimes wild: Weak continuity, Bulletin of the London Mathematical Society (2025) | DOI:10.1112/blms.70019
  • Molla, A.; Nicolay, S. The monomial functional equation for connected Lie groups, Aequationes mathematicae, Volume 98 (2024) no. 2, p. 625 | DOI:10.1007/s00010-023-00969-8
  • Chen, Jing; Yi, Taishan; Zou, Xingfu A generalization of Darboux-Froda theorem and its applications, Proceedings of the American Mathematical Society, Volume 152 (2024) no. 11, p. 4675 | DOI:10.1090/proc/16931
  • SANDERS, SAM APPROXIMATION THEOREMS THROUGHOUT REVERSE MATHEMATICS, The Journal of Symbolic Logic (2024), p. 1 | DOI:10.1017/jsl.2024.51
  • SANDERS, SAM BIG IN REVERSE MATHEMATICS: THE UNCOUNTABILITY OF THE REALS, The Journal of Symbolic Logic, Volume 89 (2024) no. 4, p. 1607 | DOI:10.1017/jsl.2023.42
  • Lalín, Matilde; Nair, Siva Sankar An invariant property of Mahler measure, Bulletin of the London Mathematical Society, Volume 55 (2023) no. 3, p. 1129 | DOI:10.1112/blms.12778
  • Cvetkovic, Marija Comparison of F-contraction and φ-contractions, Filomat, Volume 37 (2023) no. 12, p. 3951 | DOI:10.2298/fil2312951c
  • Pan, Cheng-Han Nowhere-monotone differentiable functions and set of monstrous shift, Journal of Mathematical Analysis and Applications, Volume 525 (2023) no. 2, p. 127176 | DOI:10.1016/j.jmaa.2023.127176
  • Balazard, Michel On the Infimum of the Absolute Value of Successive Derivatives of a Real Function Defined on a Bounded Interval, Number Theory in Memory of Eduard Wirsing (2023), p. 27 | DOI:10.1007/978-3-031-31617-3_4
  • SANDERS, SAM BIG IN REVERSE MATHEMATICS: MEASURE AND CATEGORY, The Journal of Symbolic Logic (2023), p. 1 | DOI:10.1017/jsl.2023.65
  • Navascués, María A. Fractal Curves on Banach Algebras, Fractal and Fractional, Volume 6 (2022) no. 12, p. 722 | DOI:10.3390/fractalfract6120722
  • Albkwre, Gbrel M.; Ciesielski, Krzysztof Chris c-lineability: A general method and its application to Darboux-like maps, Journal of Mathematical Analysis and Applications, Volume 505 (2022) no. 2, p. 125611 | DOI:10.1016/j.jmaa.2021.125611
  • Albkwre, Gbrel M.; Ciesielski, Krzysztof Chris Maximal lineability of several subclasses of Darboux-like maps on R, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, Volume 116 (2022) no. 1 | DOI:10.1007/s13398-021-01169-2
  • Albkwre, Gbrel M.; Ciesielski, Krzysztof Chris Maximal lineability of the classes of functions in the algebra of Darboux-like maps that are Darboux but not connectivity, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, Volume 116 (2022) no. 2 | DOI:10.1007/s13398-022-01226-4
  • Klyuev, A. L.; Davydov, A. D.; Grafov, B. M. Relationship Between the Structure Function of Random Time Series and the Discrete Chebyshev Spectrum, Fluctuation and Noise Letters, Volume 20 (2021) no. 03, p. 2150029 | DOI:10.1142/s0219477521500292
  • Gu, Jarry; Lalín, Matilde The Mahler measure of a three-variable family and an application to the Boyd–Lawton formula, Research in Number Theory, Volume 7 (2021) no. 1 | DOI:10.1007/s40993-021-00237-1
  • Ciesielski, K. C.; Natkaniec, T.; Rodríguez-Vidanes, D. L.; Seoane-Sepúlveda, J. B. Additivity Coefficients for all Classes in the Algebra of Darboux-Like Maps on R, Results in Mathematics, Volume 76 (2021) no. 1 | DOI:10.1007/s00025-020-01287-0
  • Gorinov, Alexey; Howard, Ralph; Johnson, Virginia; McNulty, George F. Maps That Must Be Affine or Conjugate Affine: A Problem of Vladimir Arnold, Arnold Mathematical Journal, Volume 6 (2020) no. 2, p. 213 | DOI:10.1007/s40598-020-00147-7
  • Ciesielski, Krzysztof Chris; Pan, Cheng-Han Examples of Sierpiński–Zygmund maps in the class of Darboux-like functions, Banach Journal of Mathematical Analysis, Volume 14 (2020) no. 2, p. 433 | DOI:10.1007/s43037-019-00001-9
  • Nystedt, P. Poisson's fundamental theorem of calculus via Taylor's formula, International Journal of Mathematical Education in Science and Technology, Volume 51 (2020) no. 5, p. 799 | DOI:10.1080/0020739x.2019.1682699
  • Albkwre, Gbrel M.; Ciesielski, Krzysztof Chris; Wojciechowski, Jerzy Lineability of the functions that are Sierpiński–Zygmund, Darboux, but not connectivity, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, Volume 114 (2020) no. 3 | DOI:10.1007/s13398-020-00881-9
  • Ciesielski, Krzysztof Chris; Liu, Yichen Distinct Continuous Maps with All Riemann Sums Equal, The American Mathematical Monthly, Volume 127 (2020) no. 9, p. 807 | DOI:10.1080/00029890.2020.1807290
  • Ciesielski, K.C.; Rodríguez-Vidanes, D.L.; Seoane-Sepúlveda, J.B. Algebras of measurable extendable functions of maximal cardinality, Linear Algebra and its Applications, Volume 565 (2019), p. 258 | DOI:10.1016/j.laa.2018.12.017
  • Howard, Ralph; Johnson, Virginia; McNulty, George F. A Functional Equation Characterization of Archimedean Ordered Fields, The American Mathematical Monthly, Volume 125 (2018) no. 2, p. 169 | DOI:10.1080/00029890.2018.1401877
  • SERBENYUK, S.O. Non-Differentiable Functions Defined in Terms of Classical Representations of Real Numbers, Zurnal matematiceskoj fiziki, analiza, geometrii, Volume 14 (2018) no. 2, p. 197 | DOI:10.15407/mag14.02.197
  • Harper, J F Defining continuity of real functions of real variables, BSHM Bulletin: Journal of the British Society for the History of Mathematics, Volume 31 (2016) no. 3, p. 189 | DOI:10.1080/17498430.2015.1116053
  • Marciniak, Mariola; Szczuka, Paulina A-Darboux functions, Lithuanian Mathematical Journal, Volume 56 (2016) no. 1, p. 107 | DOI:10.1007/s10986-016-9307-2
  • Aksoy, A. G.; Almira, J. M. On Montel and Montel–Popoviciu theorems in several variables, Aequationes mathematicae, Volume 89 (2015) no. 5, p. 1335 | DOI:10.1007/s00010-014-0329-8
  • Jarnicki, Marek; Pflug, Peter RETRACTED CHAPTER: Introduction: A Historical Journey, Continuous Nowhere Differentiable Functions (2015), p. 1 | DOI:10.1007/978-3-319-12670-8_1
  • Jarnicki, Marek; Pflug, Peter Baire Category Approach, Continuous Nowhere Differentiable Functions (2015), p. 107 | DOI:10.1007/978-3-319-12670-8_7
  • Jarnicki, Marek; Pflug, Peter Takagi–van der Waerden-Type Functions II, Continuous Nowhere Differentiable Functions (2015), p. 187 | DOI:10.1007/978-3-319-12670-8_9
  • Jarnicki, Marek; Pflug, Peter Bolzano-Type Functions II, Continuous Nowhere Differentiable Functions (2015), p. 203 | DOI:10.1007/978-3-319-12670-8_10
  • Jarnicki, Marek; Pflug, Peter Linear Spaces of Nowhere Differentiable Functions, Continuous Nowhere Differentiable Functions (2015), p. 245 | DOI:10.1007/978-3-319-12670-8_12
  • Jarnicki, Marek; Pflug, Peter Other Examples, Continuous Nowhere Differentiable Functions (2015), p. 99 | DOI:10.1007/978-3-319-12670-8_6
  • References, Lower Previsions (2014), p. 398 | DOI:10.1002/9781118762622.refs
  • Bingham, N. H.; Ostaszewski, A. J. Beurling slow and regular variation, Transactions of the London Mathematical Society, Volume 1 (2014) no. 1, p. 29 | DOI:10.1112/tlms/tlu002
  • Giménez, José; López, Lorena; Merentes, N. The Nemitskij operator on Lipk -type and BVk -type spaces, Demonstratio Mathematica, Volume 46 (2013) no. 3, p. 543 | DOI:10.1515/dema-2013-0465
  • Almira, Jose María; Abu-Helaiel, Khader Faiez A Note on Monomials, Mediterranean Journal of Mathematics, Volume 10 (2013) no. 2, p. 779 | DOI:10.1007/s00009-012-0215-3
  • Hairer, Ernst; Wanner, Gerhard Grundlagen der klassischen Analysis, Analysis in historischer Entwicklung (2011), p. 185 | DOI:10.1007/978-3-642-13767-9_3
  • Sam B. Nadler, Jr. A Proof of Darboux's Theorem, The American Mathematical Monthly, Volume 117 (2010) no. 2, p. 174 | DOI:10.4169/000298910x476086
  • de Cooman, Gert; Troffaes, Matthias C.M.; Miranda, Enrique A unifying approach to integration for bounded positive charges, Journal of Mathematical Analysis and Applications, Volume 340 (2008) no. 2, p. 982 | DOI:10.1016/j.jmaa.2007.09.026
  • Inhalte und Maße, Reelle Zahlen (2007), p. 185 | DOI:10.1007/978-3-540-45388-8_6
  • Talman, Louis A. Simpson's Rule Is Exact for Quintics, The American Mathematical Monthly, Volume 113 (2006) no. 2, p. 144 | DOI:10.1080/00029890.2006.11920288
  • Mascré, David Benhard Riemann, posthumous thesis on the representation of functions by trigonometric series (1867), Landmark Writings in Western Mathematics 1640-1940 (2005), p. 491 | DOI:10.1016/b978-044450871-3/50119-4
  • Cooke, Roger Henri Lebesgue and René Baire, three books on mathematical analysis (1904–1906), Landmark Writings in Western Mathematics 1640-1940 (2005), p. 757 | DOI:10.1016/b978-044450871-3/50140-6
  • Henstock, Ralph Introduction to the new integrals, New Integrals, Volume 1419 (1990), p. 7 | DOI:10.1007/bfb0083094
  • Volkert, Klaus Zur Differenzierbarkeit stetiger Funktionen ? Amp�re's Beweis und seine Folgen, Archive for History of Exact Sciences, Volume 40 (1989) no. 1, p. 37 | DOI:10.1007/bf00738359
  • Volkert, Klaus Die Geschichte der pathologischen Funktionen ? Ein Beitrag zur Entstehung der mathematischen Methodologie, Archive for History of Exact Sciences, Volume 37 (1987) no. 3, p. 193 | DOI:10.1007/bf00329901
  • Коляда, В. И. О метрическом свойст ве Дарбу, Analysis Mathematica, Volume 9 (1983) no. 4, p. 291 | DOI:10.1007/bf01910308
  • Knobloch, Eberhard Von riemann zu lebesgue—Zur entwicklung der integrationstheorie, Historia Mathematica, Volume 10 (1983) no. 3, p. 318 | DOI:10.1016/0315-0860(83)90081-2
  • Bibliography, An Introduction to Classical Complex Analysis, Volume 82 (1979), p. 462 | DOI:10.1016/s0079-8169(08)61293-3
  • Edwards, C. H. The Calculus According to Cauchy, Riemann, and Weierstrass, The Historical Development of the Calculus (1979), p. 301 | DOI:10.1007/978-1-4612-6230-5_11
  • Dugac, Pierre Notes et documents sur la vie et l'?uvre de Ren� Baire, Archive for History of Exact Sciences, Volume 15 (1976) no. 4, p. 297 | DOI:10.1007/bf00328176
  • Bruckner, Andrew M. Derivatives: Why They Elude Classification, Mathematics Magazine, Volume 49 (1976) no. 1, p. 5 | DOI:10.1080/0025570x.1976.11976524
  • Dugac, Pierre El�ments d'analyse de Karl Weierstrass, Archive for History of Exact Sciences, Volume 10 (1973) no. 1-2, p. 41 | DOI:10.1007/bf00343406
  • Monna, A. F. The concept of function in the 19th and 20th centuries, in particular with regard to the discussions between Baire, Borel and Lebesgue, Archive for History of Exact Sciences, Volume 9 (1972) no. 1, p. 57 | DOI:10.1007/bf00348540
  • Lebesgue, Henri The integral from Riemann to Bourbaki, Sets and integration An outline of the development (1972), p. 75 | DOI:10.1007/978-94-010-2718-2_2
  • CONCLUSION, Classical and Modern Integration Theories (1970), p. 178 | DOI:10.1016/b978-0-12-552550-3.50018-7
  • Halperin, Israel Discontinuous Functions with the Darboux Property, Canadian Mathematical Bulletin, Volume 2 (1959) no. 2, p. 111 | DOI:10.4153/cmb-1959-016-1
  • Lebesgue, H. Intégrale, Longueur, Aire, Annali di Matematica Pura ed Applicata, Volume 7 (1902) no. 1, p. 231 | DOI:10.1007/bf02420592
  • Albeggiani, G. Adunanza del 14 Luglio 1889, Rendiconti del Circolo Matematico di Palermo, Volume 3 (1889) no. 1, p. 273 | DOI:10.1007/bf03011527

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