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I´ll refering to "continuous" functions $$ f:R \to R $$ with it´s usual topology I've heard that using power series, can be simplified a lot of work to build a certain type of functions, like using the uniform convergence theorem for sequences of continuous functions. For example, I have asked if I can build a function that has local maxima in the rational (need not be using this, but it is the hint) and another in the set $$ \left\{ {\frac{1} {n}} \right\} \cup \left\{ 0 \right\} $$

may be useful to use these techniques?

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Could you please be a little more specific? What are you trying to do? –  Henning Makholm Sep 29 '11 at 3:23
Construct such functions, if it´s possible using this tools, but if you know other way, it´s also welcome –  August Sep 29 '11 at 3:28
It is still very unclear (atleast to me) what exactly you are trying to show/construct here. Do you wan't to build a function with with a local maxima in the rationals and one in the given set (which consists of rationals by the way)? And how is this related to measure-theory? –  Thomas E. Jun 14 '12 at 18:42

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