Chakrabarti, P. S. On properties of Peano derivatives. (English) Zbl 0406.26006 Acta Math. Acad. Sci. Hung. 32, 217-228 (1978). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page MSC: 26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems 26A21 Classification of real functions; Baire classification of sets and functions Keywords:Approximate Peano Derivative; Baire Class 1; Darboux Property; Mean Value Property; Denjoy Property; Dini Deriatives; Zahorski’s Property M2; Zahorski’s Property M3 PDFBibTeX XMLCite \textit{P. S. Chakrabarti}, Acta Math. Acad. Sci. Hung. 32, 217--228 (1978; Zbl 0406.26006) Full Text: DOI References: [1] A. M. Bruckner, J. G. Ceder andM. Weiss, Uniform limits of Darboux functions,Colloq. Math., (1966), 65–77. · Zbl 0138.28004 [2] A. Denjoy, Sur l’integration des coefficients differentiels d’order superieur,Fund. Math.,25 (1935), 273–326. [3] A. Denjoy, Sur une propriete des fonctions derivees exactesEnseignement Math.,18 (1916), 320–328. [4] M. J. Evans,L p -derivatives and approximate Peano derivatives.Trans. Amer. Math. Soc.,165 (1972), 381–388. · Zbl 0229.26009 [5] C. Goffman andC. J. Neugebauer, On approximate derivatives,Proc. Amer. Math. Soc.,11 (1960), 962–966. · Zbl 0097.26901 · doi:10.1090/S0002-9939-1960-0118792-2 [6] A. Khintchine, Recherches sur la structure des fonctions mesurables,Fund., Math.,9 (1927), 212–279. · JFM 53.0229.01 [7] N. C. Manna andS. N. Mukhopadhyay, On approximate derivatives and their properties,Acta Math. Acad. Sci. Hungar.,22 (1971), 309–320. · Zbl 0243.26005 · doi:10.1007/BF01896423 [8] S. N. Mukhopadhyay, On a certain property of the derivative,Fund. Math.,67 (1970), 279–284. · Zbl 0193.35701 [9] S. N. Mukhopadhyay, On the approximate Peano derivatives,Fund. Math.,88 (1975), 133–143. · Zbl 0307.26007 [10] S. N. Mukhopadhyay, On the regularity of theP n-integral and its application to summable trigonometric series,Pacific J. Math.,55 (1974), 233–247. · Zbl 0294.26011 · doi:10.2140/pjm.1974.55.233 [11] H. W. Oliver, The exact Peano derivative,Trans. Amer. Math. Soc.,76 (1954), 444–456. · Zbl 0055.28505 · doi:10.1090/S0002-9947-1954-0062207-1 [12] S. Saks,Theory of the integrals (Warsaw, 1937). · Zbl 0017.30004 [13] C. E. Weil, On properties of derivatives,Trans. Amer. Math. Soc.,114 (1965), 363–376. · Zbl 0163.29604 · doi:10.1090/S0002-9947-1965-0176007-2 [14] Z. Zahorski, Sur la premiere derivee,Trans. Amer. Math. Soc.,69 (1950), 1–54. · Zbl 0038.20602 [15] A. Zygmund,Trigonometric Series (Cambridge, 1968). · Zbl 0157.38204 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.