Geodesic
The Newton–Leibniz formula on Banach spaces and approximation of functions of an infinite-dimensional argument
Izvestiya. Mathematics, Tome 30 (1988) no. 1, pp. 145-161 
A. V. Uglanov. The Newton–Leibniz formula on Banach spaces and approximation of functions of an infinite-dimensional argument. Izvestiya. Mathematics, Tome 30 (1988) no. 1, pp. 145-161. http://geodesic.mathdoc.fr/item/IM2_1988_30_1_a7/
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     title = {The {Newton{\textendash}Leibniz} formula on {Banach} spaces and approximation of functions of an infinite-dimensional argument},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Properties of integrals over infinite-dimensional nonlinear manifolds are analyzed. A certain double averaging operation is introduced for functions on abstract separable Banach spaces; this operation leads to uniform approximation by smooth (in the Fréchet sense) functions in the case of spaces (and certain other cases). Bibliography: 10 titles.

[1] Daletskii Yu. L., Fomin S. V., Mery i differentsialnye uravneniya v beskonechnomernykh prostranstvakh, Nauka, M., 1975, 384 pp. | MR

[2] Uglanov A. V., “Poverkhnostnye integraly v banakhovom prostranstve”, Matem. sb., 110:2 (1979), 189–217 | MR | Zbl

[3] Neve Zh., Matematicheskie osnovy teorii veroyatnostei, Mir, M., 1969, 310 pp. | MR | Zbl

[4] Efimova E. I., Uglanov A. V., “Formuly vektornogo analiza na banakhovom prostranstve”, Dokl. AN SSSR, 271:6 (1983), 1302–1306 | MR

[5] Uglanov A. V., “Odin rezultat o differentsiruemykh merakh na lineinom prostranstve”, Matem. ob., 100:2 (1976), 242–247 | MR | Zbl

[6] Uglanov A. V., “Parabolicheskie differentsialnye uravneniya vtorogo poryadka dlya obobschennykh mer na gilbertovom prostranstve”, Vestn. MGU, matem.-mekhan., 1978, no. 1, 16–22 | MR | Zbl

[7] Go Kh.-S., Gaussovskie mery v banakhovykh prostranstvakh, Mir, M., 1979, 175 pp.

[8] Edvards R. E., Funktsionalnyi analiz, Mir, M., 1969, 1071 pp.

[9] Bonic R., Frampton J., “Differentiable functions on certain Banach spaces”, Bull. Amer. Math. Soc., 71:2 (1965), 393–395 | DOI | MR | Zbl

[10] Uglanov A. V., “O delenii obobschennykh funktsii beskonechnogo chisla peremennykh na mnogochleny”, Dokl. AN SSSR, 264:5 (1982), 1096–1099 | MR | Zbl