Geodesic
On the equivalence of integral norms on the
Teoriâ slučajnyh processov, Tome 14 (2008) no. 1, pp. 7-10.

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

We prove that, for a convex product-measure $\mu$ on a locally convex space, for any set $A$ of positive measure, on the space of measurable polynomials of degree $d,$ all $L_p(\mu)$-norms coincide with the norms obtained by restricting $\mu$ to $A.$
Keywords: Convex measure, measurable polynomial, equivalent norms. 
@article{THSP_2008_14_1_a1,
     author = {Vasiliy Berezhnoy},
     title = {On the equivalence of integral norms on the},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {7--10},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2008_14_1_a1/}
}
TY  - JOUR
AU  - Vasiliy Berezhnoy
TI  - On the equivalence of integral norms on the
JO  - Teoriâ slučajnyh processov
PY  - 2008
SP  - 7
EP  - 10
VL  - 14
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2008_14_1_a1/
LA  - en
ID  - THSP_2008_14_1_a1
ER  - 
%0 Journal Article
%A Vasiliy Berezhnoy
%T On the equivalence of integral norms on the
%J Teoriâ slučajnyh processov
%D 2008
%P 7-10
%V 14
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2008_14_1_a1/
%G en
%F THSP_2008_14_1_a1
Vasiliy Berezhnoy. On the equivalence of integral norms on the. Teoriâ slučajnyh processov, Tome 14 (2008) no. 1, pp. 7-10. http://geodesic.mathdoc.fr/item/THSP_2008_14_1_a1/

[1] A. A. Dorogovtsev, “Measurable functionals and finitely absolutely continuous measures on Banach spaces”, Ukranian Math. J., 52:9 (2000), 1194-–1204 | DOI | MR | Zbl

[2] V. E. Berezhnoy, “On the equivalence of norms on the space of $\gamma$-measurable polynomials”, Moscow Univ. Bulletin. Ser. Math., 2000, no. 4, 54-–56 | MR

[3] C. Borell, “Convex measures on locally convex spaces”, Ark. Math., 12 (1974), 239-–252 | DOI | MR | Zbl

[4] V. I. Bogachev, Measure theory, v. 1,2, Springer, Berlin, 2007 | MR | Zbl

[5] S. G. Bobkov, “Remarks on the growth of $L^p$-norms of polynomials”, Lecture Notes in Math, 1745, 2000, 27-–35 | DOI | MR | Zbl

[6] V. I. Bogachev, Gaussian measures, Amer. Math. Soc., Providence, Rhode Island, 1998 | MR | Zbl