Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
injective tensor product; product of measures; tight measures; $\tau$-smooth measures; separable measures; Fubini theorem
injective tensor product; product of measures; tight measures; $\tau$-smooth measures; separable measures; Fubini theorem
Summary:
For $i=(1,2)$, let $X_{i}$ be completely regular Hausdorff spaces, $E_{i}$ quasi-complete locally convex spaces, $E=E_{1}\Breve{\otimes }E_{2}$, the completion of the their injective tensor product, $C_{b}(X_{i})$ the spaces of all bounded, scalar-valued continuous functions on $X_{i}$, and $\mu_{i}$ $E_{i}$-valued Baire measures on $X_{i}$. Under certain conditions we determine the existence of the $E$-valued product measure $\mu_{1}\otimes \mu_{2}$ and prove some properties of these measures.
References:
[1] Babiker A.G., Knowles J.D.: Functions and measures on product spaces. Mathematika 32 (1985), 60-67. DOI 10.1112/S0025579300010871 | MR 0817109 | Zbl 0578.28004
[2] Diestel J., Uhl J.J.: Vector Measures. Mathematical Surveys, no. 15, American Mathematical Society, Providence, R.I., 1977. MR 0453964 | Zbl 0521.46035
[3] Duchoň M., Kluvánek I.: Inductive tensor product of vector-valued measures. Mat. Časopis Sloven. Akad. Vied 17 (1967), 108-112 20 (1972), 269-286. MR 0229786
[4] Fremlin D., Garling D., Haydon R.: Bounded measures on topological spaces. Proc. Lon. Math. Soc. 25 (1972), 115-136. DOI 10.1112/plms/s3-25.1.115 | MR 0344405 | Zbl 0236.46025
[5] Freniche F.J., García-Vázquez J.C.: The Bartle bilinear integration and Carleman operators. J. Math. Anal. Appl. 240 (1999), 324-339. DOI 10.1006/jmaa.1999.6575 | MR 1731648
[6] Grothendieck A.: Sur les applicationes linéaires faiblement compactes d'espaces du type $C(K)$. Canadian J. Math. 5 (1953), 129-173. DOI 10.4153/CJM-1953-017-4 | MR 0058866
[7] Jarchow H.: Locally Convex Spaces. B.G. Teubner, Stuttgart, 1981. MR 0632257 | Zbl 0466.46001
[8] Khurana S.S.: Topologies on spaces of continuous vector-valued functions. Trans Amer. Math. Soc. 241 (1978), 195-211. DOI 10.1090/S0002-9947-1978-0492297-X | MR 0492297
[9] Khurana S.S.: Topologies on spaces of continuous vector-valued functions II. Math. Ann. 234 (1978), 159-166. DOI 10.1007/BF01420966 | MR 0494178
[10] Khurana S.S.: A topology associated with vector measures. J. Indian Math. Soc. 45 (1981), 167-179. MR 0828869
[11] Khurana S.S.: Vector measures on topological spaces. Georgian Math. J., to appear. MR 2389030 | Zbl 1164.60002
[12] Kluvánek I, Knowles G.: Vector Measures and Control Systems. North-Holland Publishing Co., Amsterdam; American Elsevier Publishing Co., New York, 1976. MR 0499068
[13] Lewis D.R.: Integration with respect to vector measures. Pacific J. Math. 33 (1970), 157-165. DOI 10.2140/pjm.1970.33.157 | MR 0259064 | Zbl 0195.14303
[14] Phelps R.R.: Lectures on Choquet Theorem. Van Nostrand, Princeton, 1966. MR 0193470
[15] Schaefer H.H.: Topological Vector Spaces. Springer, New York-Berlin, 1971. MR 0342978 | Zbl 0983.46002
[16] Sentilles F.D.: Bounded continuous functions on completely regular spaces. Trans. Amer. Math. Soc. 168 (1972), 311-336. DOI 10.1090/S0002-9947-1972-0295065-1 | MR 0295065
[17] Wheeler R.F.: Survey of Baire measures and strict topologies. Exposition. Math. 1 (1983), 2 97-190. MR 0710569 | Zbl 0522.28009
[18] Varadarajan V.S.: Measures on topological spaces. Amer. Math. Soc. Transl. (2) 48 (1965), 161-220.
Search
Partner of
