  We show that any measure of entanglement that on pure bipartite states is
given by a strictly concave function of the reduced density matrix is
monogamous on pure tripartite states. This includes the important class of
bipartite measures of entanglement that reduce to the (von Neumann) entropy of
entanglement. Moreover, we show that the convex roof extension of such measures
(e.g., entanglement of formation) are monogamous also on \emph{mixed}
tripartite states. To prove our results, we use the definition of monogamy
without inequalities, recently put forward[Gour and Guo, Quantum \textbf{2}, 81
(2018)]. Our results promote the theme that monogamy of entanglement is a
property of quantum entanglement and not an attribute of some particular
measures of entanglement.
