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Currently I am trying to understand the concept of Selection System given in Billingsley's book "Probability and Measure". I have attached a pdf file with this post which consists on the scanned pages of this topic. I have understood it completely except one thing that how has the text calculated the values of "N_n". In the attached file there is an example 7.4 in which the values of N_1, N_2, N_3, and N_4 are given but I don't understand that how to calculate them or where have the come from though I do understand there role in the calculation of Y_n.

Thanks in advance.

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# Selection system - Gambling system

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