Integration with vector valued measures

M. M. Rao

doi:10.3934/dcds.2013.33.5429

Article Contents

2013, Volume 33, Issue 11&12: 5429-5440. Doi: 10.3934/dcds.2013.33.5429

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Integration with vector valued measures

M. M. Rao^1,

1.
Unversity of California, Riverside, Riverside, CA 92521

Received: July 31, 2011

Published: October 2013

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Abstract

Of the many variations of vector measures, the Fréchet variation is finite valued but only subadditive. Finding a `controlling' finite measure for these in several cases, it is possible to develop a useful integration of the Bartle-Dunford-Schwartz type for many linear metric spaces. These include the generalized Orlicz spaces, $L^{\varphi}(\mu)$, where $\varphi$ is a concave $\varphi$-function with applications to stochastic measures $Z(\cdot)$ into various Fréchet spaces useful in prediction theory. In particular, certain $p$-stable random measures and a (sub) class of these leading to positive infinitely divisible ones are detailed.

Keywords:

Vector measures in Fréchet spaces,
controling measures,
independently valued measures,
stochastic measures in generalized Orlicz spaces,
prediction theory.

Mathematics Subject Classification: Primary: 46G10, 60H05; Secondary: 28B05, 28C20.

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