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replaced link http://dx.doi.org.ezproxy.tcu.edu/10.1515/crll.1907.132.270 which was not working by DOI + added free eudml link
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According to P. Erdõs, A. Hajnal: On a property of families of sets, Acta Math. Acad. Sci. Hungar. 12 (1961), 87--123 (see page 90) the stronger result you formulated is a theorem of Bernstein from F. Bernstein, "Zur Theorie der trigonometrischen ReihenZur Theorie der trigonometrischen Reihen", Leipz. Bet. (Berichte über die Verhandlungen der Königl. Sächsischen Gesellschaft der Wissenschaften zu Leipzig. Math.phys. Klasse) 60 (1908), 325--338" MR, eudml. If you are looking for further results, "property B" is the keyword you need.

I presented a minicourse on some related properties of families of sets on the 7th Young Set Theory Workshop in 2014, so my slides may contain some results you are interested in.

According to P. Erdõs, A. Hajnal: On a property of families of sets, Acta Math. Acad. Sci. Hungar. 12 (1961), 87--123 (see page 90) the stronger result you formulated is a theorem of Bernstein from F. Bernstein, "Zur Theorie der trigonometrischen Reihen", Leipz. Bet. (Berichte über die Verhandlungen der Königl. Sächsischen Gesellschaft der Wissenschaften zu Leipzig. Math.phys. Klasse) 60 (1908), 325--338" MR. If you are looking for further results, "property B" is the keyword you need.

I presented a minicourse on some related properties of families of sets on the 7th Young Set Theory Workshop in 2014, so my slides may contain some results you are interested in.

According to P. Erdõs, A. Hajnal: On a property of families of sets, Acta Math. Acad. Sci. Hungar. 12 (1961), 87--123 (see page 90) the stronger result you formulated is a theorem of Bernstein from F. Bernstein, "Zur Theorie der trigonometrischen Reihen", Leipz. Bet. (Berichte über die Verhandlungen der Königl. Sächsischen Gesellschaft der Wissenschaften zu Leipzig. Math.phys. Klasse) 60 (1908), 325--338" MR, eudml. If you are looking for further results, "property B" is the keyword you need.

I presented a minicourse on some related properties of families of sets on the 7th Young Set Theory Workshop in 2014, so my slides may contain some results you are interested in.

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Bjørn Kjos-Hanssen
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According to P. Erdõs, A. Hajnal: On a property of families of sets, Acta Math. Acad. Sci. Hungar. 12 (1961), 87--123 (see page 90) the stronger result you formulated is a theorem of Bernstein from F. Bernstein, "Zur Theorie der trigonometrischen Reihen", Leipz. Bet. (Berichte über die VarhandlungenVerhandlungen der Königl. Sächsischen Gesellschaft der Wissenschaften zu Leipzig. Math.phys. Klasse) 60 (1908), 325--338" MR. If you are looking for further results, "property B" is the keyword you need.

I presented a minicourse on some related properties of families of sets on the 7th Young Set Theory Workshop in 2014, so my slides may contain some results you are interested in.

According to P. Erdõs, A. Hajnal: On a property of families of sets, Acta Math. Acad. Sci. Hungar. 12 (1961), 87--123 (see page 90) the stronger result you formulated is a theorem of Bernstein from F. Bernstein, "Zur Theorie der trigonometrischen Reihen", Leipz. Bet. (Berichte über die Varhandlungen der Königl. Sächsischen Gesellschaft der Wissenschaften zu Leipzig. Math.phys. Klasse) 60 (1908), 325--338" MR. If you are looking for further results, "property B" is the keyword you need.

I presented a minicourse on some related properties of families of sets on the 7th Young Set Theory Workshop in 2014, so my slides may contain some results you are interested in.

According to P. Erdõs, A. Hajnal: On a property of families of sets, Acta Math. Acad. Sci. Hungar. 12 (1961), 87--123 (see page 90) the stronger result you formulated is a theorem of Bernstein from F. Bernstein, "Zur Theorie der trigonometrischen Reihen", Leipz. Bet. (Berichte über die Verhandlungen der Königl. Sächsischen Gesellschaft der Wissenschaften zu Leipzig. Math.phys. Klasse) 60 (1908), 325--338" MR. If you are looking for further results, "property B" is the keyword you need.

I presented a minicourse on some related properties of families of sets on the 7th Young Set Theory Workshop in 2014, so my slides may contain some results you are interested in.

Incorporated Andreas's correction, and added links
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According to P. Erdõs, A. Hajnal: On a property of families of sets, Acta Math. Acad. Sci. Hungar. 12 (1961), 87--123 (see page 90) the stronger result you formulated is a theorem of Bernstein from "F. Bernstein, Zur Theorie der trigonometrischen Reihen"Zur Theorie der trigonometrischen Reihen", Leipz. Bet. (Beriehte tiberBerichte über die VerhandlungenVarhandlungen der K6niglKönigl. S/rSächsischen Gesellschaft der Wissensohaften zuWissenschaften zu Leipzig. Math.-phys. Klasse) 60 (1908), 325--338." MR. If you are looking for further results, "property B" is the keyword you need.

I presented a minicourse on some related properties of families of sets on the 7th Young Set Theory Workshop in 2014, so my slides may contain some results you are interested in.

According to P. Erdõs, A. Hajnal: On a property of families of sets, Acta Math. Acad. Sci. Hungar. 12 (1961), 87--123 (see page 90) the stronger result you formulated is a theorem of Bernstein from "F. Bernstein, Zur Theorie der trigonometrischen Reihen, Leipz. Bet. (Beriehte tiber die Verhandlungen der K6nigl. S/r Gesellschaft der Wissensohaften zu Leipzig. Math.-phys. Klasse) 60 (1908), 325--338." If you are looking for further results, "property B" is the keyword you need.

I presented a minicourse on some related properties of families of sets on the 7th Young Set Theory Workshop in 2014, so my slides may contain some results you are interested in.

According to P. Erdõs, A. Hajnal: On a property of families of sets, Acta Math. Acad. Sci. Hungar. 12 (1961), 87--123 (see page 90) the stronger result you formulated is a theorem of Bernstein from F. Bernstein, "Zur Theorie der trigonometrischen Reihen", Leipz. Bet. (Berichte über die Varhandlungen der Königl. Sächsischen Gesellschaft der Wissenschaften zu Leipzig. Math.phys. Klasse) 60 (1908), 325--338" MR. If you are looking for further results, "property B" is the keyword you need.

I presented a minicourse on some related properties of families of sets on the 7th Young Set Theory Workshop in 2014, so my slides may contain some results you are interested in.

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Lajos Soukup
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