Hypergraph degree measure
= Hypergraph degree measure
{title2=$\mu(S)=\frac1{nd}\sum_{u\in S}d_H(u)$}
For a <uniform hypergraph> with positive average <hypergraph vertex degree> $d$, the degree measure is $\mu(S)=(nd)^{-1}\sum_{u\in S}d_H(u)$. It is a <probability measure> and equals $|S|/n$ in a regular hypergraph. Every <hypergraph independent set> has degree measure at most $1-1/r$, even when its fraction of all vertices is close to one.