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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: a subset of continuous functions - is it interesting?
Replies: 8   Last Post: May 12, 2009 12:35 PM

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Mariano

Posts: 1,900
Registered: 8/22/05
Re: a subset of continuous functions - is it interesting?
Posted: May 11, 2009 11:57 AM
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On May 11, 12:47 pm, boyandshark <amitgan...@gmail.com> wrote:
> I want to form the following subset of the set C of continuous
> functions from R^M to R^N:
>
> The largest subset S of continuous functions such that for any two
> functions f and g in S, the set of points x in R^M for which f(x)=g(x)
> has Lebesgue measure zero.

Is it obvious that this is a good definition? I do not see
at once why there is a maximum set with that property or, even,
that there exists maximal sets with that property.

-- m

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