Abstract
Extensions of locally convex topological spaces are considered such that finite cylindrical measures which are not countably additive on their initial domains turn out to be countably additive on the extensions. Extensions of certain transformations of the initial spaces with respect to which the initial measures are invariant or quasi-invariant to the extensions of these spaces are described. Similar questions are considered for differentiable measures. The constructions may find applications in statistical mechanics and quantum field theory.
Similar content being viewed by others
References
V. V. Kozlov, Russ. Math. Surv., 63 (4), 691–726 (2008).
O. G. Smolyanov and S. V. Fomin, Russ. Math. Surv. 31 (4), 1–53 (1976).
O. G. Smolyanov and E. T. Shavgulidze, Continual Integrals, 2nd ed. (URRS, Moscow, 2015) [in Russian].
V. I. Bogachev and O. G. Smolyanov, Russ. Math. Surv. 45 (3), 1–104 (1990).
V. I. Bogachev, Differentiable Measures and the Malliavin Calculus (Am. Math. Soc., Providence, R.I., 2010).
O. G. Smolyanov, Dokl. Akad. Nauk SSSR 170 (3), 526–529 (1966).
J. Kupsch and O. G. Smolyanov, Math. Notes 68 (3), 409–414 (2000).
N. Dunford and J. Schwartz, Linear Operators, Vol. 1: General Theory (Interscience, New York, 1958).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.V. Kozlov, O.G. Smolyanov, 2015, published in Doklady Akademii Nauk, 2015, Vol. 465, No. 5, pp. 527–531.
Rights and permissions
About this article
Cite this article
Kozlov, V.V., Smolyanov, O.G. Invariant and quasi-invariant measures on infinite-dimensional spaces. Dokl. Math. 92, 743–746 (2015). https://doi.org/10.1134/S1064562415060290
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064562415060290