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# How large (small) can be the measure of a set where a polynomial takes small values

A $n$-th degree polynomial has precisely $n$ roots. So it is natural to ask the question how large ( and small) can be the measure of a set where a polynomial takes small values ?

This, and other interesting variation of this must have been studied in depth.

I would really appreciate any reference to the relevant literature.

Also, if there are some interesting variation of this problem I would like to know.

Thank you.