  We congratulate Engelke and Hitz on a thought-provoking paper on graphical
models for extremes. A key contribution of the paper is the introduction of a
novel definition of conditional independence for a multivariate Pareto
distribution. Here, we outline a proposal for independence and conditional
independence of general random variables whose support is a general set Omega
in multidimensional real number space. Our proposal includes the authors'
definition of conditional independence, and the analogous definition of
independence as special cases. By making our proposal independent of the
context of extreme value theory, we highlight the importance of the authors'
contribution beyond this particular context.
