Abstract
The space of signed measures on the Borel σ-algebra of a Polish space is incomplete with respect to the bounded Lipschitz norm. Elements of its completion are called hypermeasures. They can be regarded as linear functionals on the space of bounded Lipschitz functions. It is shown that, under mild assumptions, every stochastically continuous random linear functional on this space is a modification of a random hypermeasure.
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References
Jacod, J., Shiryaev, A.N.: Limit Theorems for Stochastic Processes. Springer, Berlin (1987)
Radchenko, V.N.: Integrals by General Random Measures. Inst. for Math. of the Nat. Acad. Sci. Ukr., Kiev (1999) (Russian)
Shylov, G.E., Gurevich, B.L.: Integral, Measure and Derivative. Nauka, Moscow (1967) (Russian)
Turpin, P.: Convéxités dans les espaces vectoriels topologiques généraux. Diss. Math. 131, 3–220 (1976)
Yurachkivsky, A.P.: The space of hypermeasures. Dopovidi Natsionalnoĭi Akademii Nauk Ukrainy [Reports of the Nat. Acad. Sci. Ukr.] No. 3, pp. 35–40 (2006) (Ukrainian)
Yurachkivsky, A.P.: Stochastic integrators and random hypermeasures. Dopovidi Natsionalnoĭi Akademii Nauk Ukrainy [Reports of the Nat. Acad. Sci. Ukr.] No. 4, pp. 26–30 (2006) (Ukrainian)
Yurachkivsky, A.P.: Random hypermeasures. In: Hušková, M., Janžura, M. (eds.) Prague Stochastics 2006. Proceedings, pp. 739–748. Matfyzpress, Prague (2006)
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Yurachkivsky, A. Random Linear Functionals Arising in Stochastic Integration. Acta Appl Math 97, 353–362 (2007). https://doi.org/10.1007/s10440-007-9115-0
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DOI: https://doi.org/10.1007/s10440-007-9115-0