edited tags; edited title
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.