Additive Functionals on Lp Spaces
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1264-1271
Voir la notice de l'article provenant de la source Cambridge University Press
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.
Friedman, N.; Katz, M. Additive Functionals on Lp Spaces. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1264-1271. doi: 10.4153/CJM-1966-125-x
@article{10_4153_CJM_1966_125_x,
author = {Friedman, N. and Katz, M.},
title = {Additive {Functionals} on {Lp} {Spaces}},
journal = {Canadian journal of mathematics},
pages = {1264--1271},
year = {1966},
volume = {18},
number = {1},
doi = {10.4153/CJM-1966-125-x},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-125-x/}
}
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[4] 4. Martin, A. D. and Mizel, V. J., A representation theorem for certain nonlinear functionals, Arch. Rational Mech. Anal., 16 (1964), 353–367. Google Scholar
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