On introduit une notion d’ensemble négligeable dans un polydisque. On démontre l’existence de “bonnes” mesures sur un ensemble non-négligeable. On l’utilise pour construire des fonctions holomorphes “good” et “good inner” dans un polydisque.
A notion of negligible sets for polydiscs is introduced. Some properties of non-negligible sets are proved. These results are used to construct good and good inner functions on polydiscs.
@article{AIF_1979__29_2_211_0,
author = {Gowrisankaran, Kohur},
title = {Negligible sets and good functions on polydiscs},
journal = {Annales de l'Institut Fourier},
volume = {29},
year = {1979},
pages = {211-222},
doi = {10.5802/aif.747},
mrnumber = {81a:32013},
zbl = {0412.31004},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_1979__29_2_211_0}
}
Gowrisankaran, Kohur. Negligible sets and good functions on polydiscs. Annales de l'Institut Fourier, Tome 29 (1979) pp. 211-222. doi : 10.5802/aif.747. http://gdmltest.u-ga.fr/item/AIF_1979__29_2_211_0/
[1] , Measurability of Functions in a Product Space, Proc. Amer. Math. Soc., 31 (1972), 485-488. | MR 45 #496 | Zbl 0229.28006
[2] , Multiply Superharmonic functions, Annales Inst. Fourier, XXV, Fasc. 3 et 4 (1975), 235-244. | Numdam | MR 53 #5918 | Zbl 0303.31006
[3] , Introduction to Potential Theory, Wiley Interscience, 1973.
[4] , Recherches sur la théorie axiomatique des fonctions harmoniques et du potential, Annales Inst. Fourier, XII (1962), 415-571. | Numdam | MR 25 #3186 | Zbl 0101.08103
[5] , Function theory in polydiscs, Benjamin, 1969. | MR 41 #501 | Zbl 0177.34101
[6] , Inner functions on Polydiscs, Ph.D. Thesis, McGill University August 1977. See also the paper in these Annales. | Numdam | Zbl 0381.32007
[7] , Radon measures on arbitrary topological spaces and cylindrical measures, Oxford Univ. Press, Bombay, 1973. | MR 54 #14030 | Zbl 0298.28001