Geodesic
Some results on differentiable measures
Sbornik. Mathematics, Tome 55 (1986) no. 2, pp. 335-349 
V. I. Bogachev. Some results on differentiable measures. Sbornik. Mathematics, Tome 55 (1986) no. 2, pp. 335-349. http://geodesic.mathdoc.fr/item/SM_1986_55_2_a2/
@article{SM_1986_55_2_a2,
     author = {V. I. Bogachev},
     title = {Some results on differentiable measures},
     journal = {Sbornik. Mathematics},
     pages = {335--349},
     year = {1986},
     volume = {55},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1986_55_2_a2/}
}
TY  - JOUR
AU  - V. I. Bogachev
TI  - Some results on differentiable measures
JO  - Sbornik. Mathematics
PY  - 1986
SP  - 335
EP  - 349
VL  - 55
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1986_55_2_a2/
LA  - en
ID  - SM_1986_55_2_a2
ER  - 
%0 Journal Article
%A V. I. Bogachev
%T Some results on differentiable measures
%J Sbornik. Mathematics
%D 1986
%P 335-349
%V 55
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1986_55_2_a2/
%G en
%F SM_1986_55_2_a2

Voir la notice de l'article provenant de la source Math-Net.Ru

Connections are described between various differentiability properties of measures on locally convex spaces. In particular, it is proved that every analytic measure is quasi-invariant, and every quasi-invariant measure is absolutely continuous with respect to some analytic measure. It is proved that for stable measures continuity in some direction implies infinite differentiability, and even analyticity in this direction when $\alpha\geqslant1$. A solution is presented for a problem posed by Aronszajn (RZh.Mat., 1977, 5B557). Bibliography: 16 titles.

[1] Aronszajn N., “Differentiability of Lipschitzian mappings between Banach spaces”, Studia Math., 57:2 (1976), 147–190 | MR | Zbl

[2] Danford N., Shvarts Dzh., Lineinye operatory. Obschaya teoriya, IL, M., 1962

[3] Romanov V. P., “Predely differentsiruemykh mer v gilbertovom prostranstve”, Ukr. mat. zhurn., 33:2 (1981), 215–219 | MR | Zbl

[4] Averbukh V. I., Smolyanov O. G., Fomin S. V., “Obobschennye funktsii i differentsialnye uravneniya v lineinykh prostranstvakh”, Tr. MMO, 24 (1971), 132–174

[5] Bentkus V. Yu., “Analitichnost gaussovskikh mer”, Teoriya veroyatnostei i ee primeneniya, 27:1 (1982), 147–154 | MR | Zbl

[6] Skorokhod A. V., Integrirovanie v gilbertovom prostranstve, Nauka, M., 1975

[7] Smolyanov O. G., Analiz na topologicheskikh lineinykh prostranstvakh i ego prilozheniya, Izd-vo MGU, M., 1979

[8] Bogachev V. I., “Prenebrezhimye mnozhestva v lokalno vypuklykh prostranstvakh”, Matem. zametki, 36:1 (1984), 51–64 | MR | Zbl

[9] Daletskii Yu. L., Fomin S. V., Mery i differentsialnye uravneniya v beskonechnomernykh prostranstvakh, Nauka, M., 1983 | MR

[10] Zolotarev V. M., Odnomernye ustoichivye raspredeleniya, Nauka, M., 1983 | MR

[11] Phelps R., “Gaussian null sets and differentiability of Lipschitz map on Banach spaces”, Pacif. J. Math., 77:2 (1978), 523–531 | MR | Zbl

[12] Shevchik V. V., “O podprostranstvakh banakhova prostranstva, sovpadayuschikh s oblastyami znachenii lineinykh nepreryvnykh operatorov”, DAN SSSR, 263:4 (1982), 817–819 | MR | Zbl

[13] Shefer Kh., Topologicheskie vektornye prostranstva, Mir, M., 1971 | MR

[14] Distel Dzh., Geometriya banakhovykh prostranstv, Vischa shkola, Kiev, 1980 | MR

[15] Pich A., Yadernye lokalno vypuklye prostranstva, Mir, M., 1967 | MR

[16] Sudakov V. N., “Geometricheskie problemy beskonechnomernykh raspredelenii”, Tr. MIAN, CX:1 (1976), 1–190