  We analyse two possible definitions of the squashed entanglement in an
infinite-dimensional bipartite system: direct translation of the
finite-dimensional definition and its universal extension. It is shown that the
both definitions produce the same lower semicontinuous entanglement measure
possessing all basis properties of the squashed entanglement on the set of
states having at least one finite marginal entropy. Is also shown that the
second definition gives an adequate extension of this measure to the set of all
states of infinite-dimensional bipartite system.
  A general condition relating continuity of the squashed entanglement to
continuity of the quantum mutual information is proved and its corollaries are
considered.
  Continuity bound for the squashed entanglement under the energy constraint on
one subsystem is obtained by using the tight continuity bound for conditional
mutual information (proved in the Appendix by using Winter's technique). It is
shown that the same continuity bound is valid for the entanglement of
formation. As a result the asymptotic continuity of the both entanglement
measures under the energy constraint on one subsystem is proved.
