Measure estimate for $p$-adic Diophantine approximation

A quantitative estimate for the measure of the set of $p$-adic numbers for which the inequality $|P(x)|_p<Q^{-w}$ for $w>3n/2+2$ has a solution in integral polynomials P of degree n and of height $H(P)$ at most $Q\in\mathbb{N}$, is established.