## another question from distribution of reals corresponding to set of the original version [closed]

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distribution of reals corresponding to set

given S set of natural number ,the corresponding real in interval (0,1] of S can be regarded the continued fraction $1/(a_0+1/(a_1+...))$ where the $a_i$ are the elements of S in increasing order .using the uniform measure on subsets of N:how about the measure of the reals of the reals if S is productive set?.How about the measure of the reals if S is immune set?How the measure of the reals of the reals if S is neither immune set nor productive set nor c.e.set?

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Thank Mr.Andreas Blass ,Andrej Bauer,Andres Caicedo,Gerry Myerson for their comments and suggests (see discussion of the original question below),and me ,who have never been so patient to rephrase question or articles . – XL Apr 14 2011 at 2:13
This one is mainly resulted from Mr.Andreas Blass's comment . – XL Apr 14 2011 at 3:00
Please use the "edit" link below the original question to revise it, instead of adding a new question. – S. Carnahan Apr 14 2011 at 7:31