no. 2
Negligible sets and good functions on polydiscs
Annales de l'Institut Fourier, Tome 29 (1979) no. 2, pp. 211-222.

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.

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     title = {Negligible sets and good functions on polydiscs},
     journal = {Annales de l'Institut Fourier},
     pages = {211--222},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {29},
     number = {2},
     year = {1979},
     doi = {10.5802/aif.747},
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Gowrisankaran, Kohur. Negligible sets and good functions on polydiscs. Annales de l'Institut Fourier, Tome 29 (1979) no. 2, pp. 211-222. doi : 10.5802/aif.747. https://aif.centre-mersenne.org/articles/10.5802/aif.747/

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

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

[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 | Zbl

[5] W. Rudin, Function theory in polydiscs, Benjamin, 1969. | MR | Zbl

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

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

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