Geodesic
Maharam-Types and Lyapunov's Theorem for Vector Measures on Locally Convex Spaces with Control Measures
Journal of convex analysis, Tome 22 (2015) no. 3, pp. 647-672
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This paper presents an equivalence between (i) the Lyapunov property under which a vector measure with values in a sequentially complete, separable locally convex Hausdorff space (lcHs) has a weakly compact and convex range, (ii) the thinness property of subsets of Bochner integrable functions due to Kingman-Robertson (1968) and (iii) the saturation property due to Maharam (1942) and Hoover-Keisler (1984). It also considers the case of a non-separable range space, and presents versions of the Lyapunov theorem for a quasicomplete lcHs based either on the Egorov property or the notion of Maharam-types. The results are applied to two canonical objects in convex analysis: the integral and the distribution of a multifunction.
Classification : 28B05, 46G10, 28B20, 46B22
Mots-clés : Saturation property, Lyapunov's theorem, locally convex space, thin sets, integral, distribution, multifunction, Radon-Nikodym property, control measure, Maharam-type 
@article{JCA_2015_22_3_JCA_2015_22_3_a3,
     author = {M. A. Khan and N. Sagara},
     title = {Maharam-Types and {Lyapunov's} {Theorem} for {Vector} {Measures} on {Locally} {Convex} {Spaces} with {Control} {Measures}},
     journal = {Journal of convex analysis},
     pages = {647--672},
     year = {2015},
     volume = {22},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2015_22_3_JCA_2015_22_3_a3/}
}
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M. A. Khan; N. Sagara. Maharam-Types and Lyapunov's Theorem for Vector Measures on Locally Convex Spaces with Control Measures. Journal of convex analysis, Tome 22 (2015) no. 3, pp. 647-672. http://geodesic.mathdoc.fr/item/JCA_2015_22_3_JCA_2015_22_3_a3/