  Given an algebroid plane curve $f=0$ over an algebraically closed field of
characteristic $p\geq 0$ we consider the Milnor number $\mu(f)$, the delta
invariant $\delta(f)$ and the number $r(f)$ of its irreducible components. Put
$\bar \mu(f)=2\delta(f)-r(f)+1$. If $p=0$ then $\bar \mu (f)=\mu(f)$ (the
Milnor formula). If $p>0$ then $\mu(f)$ is not an invariant and $\bar \mu(f)$
plays the role of $\mu(f)$. Let $\mathcal N_f$ be the Newton polygon of $f$. We
define the numbers $\mu(\mathcal N_{f})$ and $r(\mathcal N_{f})$ which can be
computed by explicit formulas. The aim of this note is to give a simple proof
of the inequality $\bar \mu(f)-\mu(\mathcal N_{f})\geq r(\mathcal N_{f})-
r(f)\geq 0$ due to Boubakri, Greuel and Markwig. We also prove that $\bar
\mu(f)=\mu(\mathcal N_{f})$ when $f$ is non-degenerate.
