Analysis on some linear sets
Kaufman, Robert
Annales de l'Institut Fourier, Tome 21 (1971), p. 23-29 / Harvested from Numdam

On construit des ensembles aléatoires de multiplicité rationnellement indépendants, précisant ces propriétés sous deux aspects techniques. On améliore quelques résultats obtenus par les processus gaussiens ou la méthode topologique de catégorie.

The note discusses a probabilistic method for constructing “small” sets, with regard to differentiable transformations and to quantitative measures of independence.

@article{AIF_1971__21_2_23_0,
     author = {Kaufman, Robert},
     title = {Analysis on some linear sets},
     journal = {Annales de l'Institut Fourier},
     volume = {21},
     year = {1971},
     pages = {23-29},
     doi = {10.5802/aif.370},
     mrnumber = {49 \#5677},
     zbl = {0215.25403},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1971__21_2_23_0}
}
Kaufman, Robert. Analysis on some linear sets. Annales de l'Institut Fourier, Tome 21 (1971) pp. 23-29. doi : 10.5802/aif.370. http://gdmltest.u-ga.fr/item/AIF_1971__21_2_23_0/

[1] J. W. S. Cassels, An introduction to Diophantine approximation, Cambridge Tract 45, (1957). | MR 19,396h | Zbl 0077.04801

[2] H. Davenport, A note on Diophantine approximation II. Mathematika 11 (1964), 50-58. | MR 29 #3432 | Zbl 0122.05903

[3] J.-P. Kahane, Images browniennes des ensembles parfaits, C.R. Acad. Sci., Paris 263A (1966), 613-615. | MR 35 #3752 | Zbl 0158.35703

[4] J.-P. Kahane and R. Salem, Ensembles parfaits, Hermann, Paris, 1963. | Zbl 0112.29304

[5] N. Th. Varopoulos, Sets of multiplicity in locally compact abelian groups, Ann. Inst. Fourier (Grenoble) 16 (1966), 123-158. | Numdam | MR 35 #3379 | Zbl 0145.03501

[6] A. Zygmund, Trigonometric Series, Cambridge, (1959, 1968). | Zbl 0085.05601