  We define the independent natural extension of two local models for the
general case of infinite spaces, using both sets of desirable gambles and
conditional lower previsions. In contrast to Miranda and Zaffalon (2015), we
adopt Williams-coherence instead of Walley-coherence. We show that our notion
of independent natural extension always exists - whereas theirs does not - and
that it satisfies various convenient properties, including factorisation and
external additivity.
