Journal of the Ramanujan Mathematical Society

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Multiplicative Integral via Finitely Multiplicative Measures


Affiliations
1 Department of Mathematics, University of Wisconsin at Superior, Superior, Wisconsin 54880, United States
2 Department of Mathematics, University of Georgia, Athens, 30602, Georgia
     

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We introduce a multiplicative integral (better known as product integral) using the notion of finitely multiplicative measures which are essentially "exponentials" of operator valued measures. This approach enables us to recover, as special cases, the multiplicative integrals of Dollard-Friedman and Masani; moreover, it directly extends to stochastic cases and allows us to compare the multiplicative integral with (usual) additive integral. Along with other properties of our multiplicative integral, we also establish a Peano series theorem which in turn is utilized to solve an integral equation.
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  • Multiplicative Integral via Finitely Multiplicative Measures

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Authors

L. Hazareesingh
Department of Mathematics, University of Wisconsin at Superior, Superior, Wisconsin 54880, United States
D. Kannan
Department of Mathematics, University of Georgia, Athens, 30602, Georgia

Abstract


We introduce a multiplicative integral (better known as product integral) using the notion of finitely multiplicative measures which are essentially "exponentials" of operator valued measures. This approach enables us to recover, as special cases, the multiplicative integrals of Dollard-Friedman and Masani; moreover, it directly extends to stochastic cases and allows us to compare the multiplicative integral with (usual) additive integral. Along with other properties of our multiplicative integral, we also establish a Peano series theorem which in turn is utilized to solve an integral equation.