Additive Functionals on Lp Spaces
1966 ◽
Vol 18
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pp. 1264-1271
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In (1) a representation theorem was proved for a class of additive functionals defined on the continuous real-valued functions with domain S = [0, 1]. The theorem was extended to the case where S is an arbitrary compact metric space in (3). Our present purpose is to consider the corresponding class of additive functionals defined on Lp spaces, p > 0. In (4) Martin and Mizel have considered functionals defined on the class of bounded measurable functions which, however, satisfy a certain “stochastic” condition which we do not require.
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2015 ◽
Vol 9
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pp. 19-29
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