Diverses techniques sont présentées pour la construction d’ensembles que ne sont pas quel que soit . Il en résulte essentiellement qu’il existe un ensemble dans le dual de tout groupe abélien compact qui n’est pas quel que soit . Au cours de la démonstration de nouvelles constructions sont données en groupes duaux dans lesquels des constructions d’ensembles et non étaient déjà connues, pour certaines valeurs de . Les principales nouvelles constructions en groupes duaux sont :
– il existe un ensemble qui n’est pas en quel que soit , et ainsi que dans ( étant un nombre premier, ) pour , et (pour répondre à une question posée dans J. Lopez and K. Ross, Marcel Dekker, 1975),
– il existe un ensemble qui n’est pas dans pour , et tout .
Il est également démontré que des suites aléatoires illimitées en entiers sont et non pas pour , et .
Various techniques are presented for constructing (p) sets which are not for all . The main result is that there is a (4) set in the dual of any compact abelian group which is not for all . Along the way to proving this, new constructions are given in dual groups in which constructions were already known of (p) not sets, for certain values of . The main new constructions in specific dual groups are:
– there is a (2k) set which is not in for all , and , and in ( a prime, ) for , and (answering a question in J. Lopez and K. Ross, Marcel Dekker, 1975),
– there is a (2k) set which is not in for , and all
It is also shown that random infinite integer sequences are (2k) but not for , and .
@article{AIF_1986__36_3_137_0, author = {Hajela, D. J.}, title = {Construction techniques for some thin sets in duals of compact abelian groups}, journal = {Annales de l'Institut Fourier}, pages = {137--166}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {36}, number = {3}, year = {1986}, doi = {10.5802/aif.1063}, zbl = {0586.43004}, mrnumber = {88c:43007}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1063/} }
TY - JOUR AU - Hajela, D. J. TI - Construction techniques for some thin sets in duals of compact abelian groups JO - Annales de l'Institut Fourier PY - 1986 SP - 137 EP - 166 VL - 36 IS - 3 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1063/ DO - 10.5802/aif.1063 LA - en ID - AIF_1986__36_3_137_0 ER -
%0 Journal Article %A Hajela, D. J. %T Construction techniques for some thin sets in duals of compact abelian groups %J Annales de l'Institut Fourier %D 1986 %P 137-166 %V 36 %N 3 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.1063/ %R 10.5802/aif.1063 %G en %F AIF_1986__36_3_137_0
Hajela, D. J. Construction techniques for some thin sets in duals of compact abelian groups. Annales de l'Institut Fourier, Tome 36 (1986) no. 3, pp. 137-166. doi : 10.5802/aif.1063. https://aif.centre-mersenne.org/articles/10.5802/aif.1063/
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