Negligible sets and good functions on polydiscs
Annales de l'Institut Fourier, Volume 29 (1979) no. 2, p. 211-222
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.
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.
@article{AIF_1979__29_2_211_0,
     author = {Gowrisankaran, Kohur},
     title = {Negligible sets and good functions on polydiscs},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {29},
     number = {2},
     year = {1979},
     pages = {211-222},
     doi = {10.5802/aif.747},
     zbl = {0412.31004},
     mrnumber = {81a:32013},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1979__29_2_211_0}
}
Gowrisankaran, Kohur. Negligible sets and good functions on polydiscs. Annales de l'Institut Fourier, Volume 29 (1979) no. 2, pp. 211-222. doi : 10.5802/aif.747. http://www.numdam.org/item/AIF_1979__29_2_211_0/

[1] K. Gowrisankaran, Measurability of Functions in a Product Space, Proc. Amer. Math. Soc., 31 (1972), 485-488. | MR 45 #496 | Zbl 0229.28006

[2] K. Gowrisankaran, Multiply Superharmonic functions, Annales Inst. Fourier, XXV, Fasc. 3 et 4 (1975), 235-244. | Numdam | MR 53 #5918 | Zbl 0303.31006

[3] L.L. Helms, Introduction to Potential Theory, Wiley Interscience, 1973.

[4] R. M. Hervé, 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] W. Rudin, Function theory in polydiscs, Benjamin, 1969. | MR 41 #501 | Zbl 0177.34101

[6] E. Sawyer, Inner functions on Polydiscs, Ph.D. Thesis, McGill University August 1977. See also the paper in these Annales. | Numdam | Zbl 0381.32007

[7] L. Schwartz, Radon measures on arbitrary topological spaces and cylindrical measures, Oxford Univ. Press, Bombay, 1973. | MR 54 #14030 | Zbl 0298.28001