Abstract
Let X and Y be Banach spaces. An integration theory is presented which gives a concrete representation of the completion of the space of X-valued, simple functions for the mean convergence with respect to a Y-valued measure. Functions integrated take values in a locally convex space which contains a copy of X.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R.G. Bartle, A general bilinear vector integral, Studia Math., 15 (1956), 337–352.
J. Diestel and J.J. Uhl, Jr., Vector Measures, Math. Surveys, no. 15, Amer. Math. Soc., Providence, 1977.
I. Dobrakov, On integration in Banach spaces, I, Czech. Math. J. 20 (95)(1970), 511–536.
M. Duchoň, A dominancy of vector-valued measures, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 19 (1971), 1085–1091.
H. Jakobs, Ordered topological tensor products, Ph.D. thesis, University of Illinois at Urbana-Champaign, Urbana, 1969.
I. Kluvánek and G. Knowles, Vector Measures and Control Systems, North Holland, Amsterdam, 1975.
G. Köthe, Topological Vector Spaces II, Springer-Verlag, New York, 1979.
J. Mikusiński, The Bochner Integral, Birkhäuser Verlag, Basel, 1978.
S. Okada, Integration of vector-valued functions, to appear in Proc. Workshop on Measure Theory and its Appl., University de Sherbrooke, Lecture Note in Math., Springer-Verlag, Berlin and New York.
C. Swartz, A generalization of a theorem of Duchoň on products of vector measures, J. Math. Anal. and Appl., 51 (1975), 621–628.
G.E.F. Thomas, Integration of functions with values in locally convex Suslin spaces, Trans. Amer. Math. Soc., 212 (1975), 61–81.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1984 Springer-Verlag
About this paper
Cite this paper
Okada, S. (1984). A tensor product vector integral. In: Kölzow, D., Maharam-Stone, D. (eds) Measure Theory Oberwolfach 1983. Lecture Notes in Mathematics, vol 1089. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072609
Download citation
DOI: https://doi.org/10.1007/BFb0072609
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-13874-7
Online ISBN: 978-3-540-39069-5
eBook Packages: Springer Book Archive