  We show that a Borel action of a standard Borel group which is isomorphic to
a sum of a countable abelian group with a countable sum of real lines and
circles induces an orbit equivalence relation which is hypersmooth, i.e., Borel
reducible to eventual agreement on sequences of reals, and it follows from this
result along with the structure theory for locally compact abelian groups that
Borel actions of Polish LCA groups induce orbit equivalence relations which are
essentially hyperfinite, extending a result of Gao and Jackson and answering a
question of Ding and Gao.
