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Thesis
editI have talked to Steven Gaal, he says that it is inaccuarate in that his thesis is not the joint paper mentioned.
I also noticed that looking at the referenced paper that the link only goes to the first part: http://www.renyi.hu/~p_erdos/1955-06.pdf but there is also a second part: http://www.renyi.hu/~p_erdos/1955-07.pdf