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