# Are almost everywhere equal functions asymptotic?

I'm quite new at measure theory and all I know I read by myself, so bear with me if this question is too trivial.

Given the definition of asymptotic, can we say that for $x \rightarrow \infty$ two almost everywhere equal functions are asymptotic? I really think that this is not the case, but I haven't been able to find a counterexample. Maybe, if in general this does not hold, would it be right for real functions?

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