  We show global uniqueness in the fractional Calder\'on problem with a single
measurement and with data on arbitrary, possibly disjoint subsets of the
exterior. The previous work \cite{GhoshSaloUhlmann} considered the case of
infinitely many measurements. The method is again based on the strong
uniqueness properties for the fractional equation, this time combined with a
unique continuation principle from sets of measure zero. We also give a
constructive procedure for determining an unknown potential from a single
exterior measurement, based on constructive versions of the unique continuation
result that involve different regularization schemes.
