Heights of an extension (awaiting review)

Let $L/K$ be an extension of $p$-adic fields. The height $H(L/K)$ of $L/K$ is defined by the formula $c=f(e−1+H(L/K))$, where $c$ is the discriminant exponent, $f$ the residue field degree, and $e$ the ramification degree of $L/K$. Since $H(L/K)$ is 0 if $L/K$ is tamely ramified, and positive otherwise, $H(L/K)$ is a measure of the wild ramification of $L/K$.

Now let $K\subset L_1\subset\dots\subset L_r=L$ be the sequence of subextensions of $L/K$ which correspond to the segments of the ramification polygon of $L/K$. The set of heights for $L/K$ is $\{H(L_i/K):1\le i\le r\}$.