  The stellar mass in the halo of the Milky Way is notoriously difficult to
determine, owing to the paucity of its stars in the solar neighbourhood. With
tentative evidence from $\it{Gaia}$ that the nearby stellar halo is dominated
by a massive accretion event -- referred to as $\it{Gaia-Enceladus}$ or Sausage
-- these constraints are now increasingly urgent. We measure the mass in
kinematically selected mono-abundance populations (MAPs) of the stellar halo
between $-3 <$ [Fe/H] $< -1$ and $0.0 <$ [Mg/Fe] $< 0.4$ using red giant star
counts from APOGEE DR14. We find that MAPs are well fit by single power laws on
triaxial ellipsoidal surfaces, and we show that that the power law slope
$\alpha$ changes such that high $\mathrm{[Mg/Fe]}$ populations have $\alpha
\sim 4$, whereas low [Mg/Fe] MAPs are more extended with shallow slopes,
$\alpha \sim 2$. We estimate the total stellar mass to be $M_{*,\mathrm{tot}} =
1.3^{+0.3}_{-0.2}\times10^{9}\ \mathrm{M_{\odot}}$, of which we estimate $\sim
0.9^{+0.2}_{-0.1} \times 10^{9} \mathrm{M_{\odot}}$ to be accreted. We estimate
that the mass of accreted stars with $e > 0.7$ is
$M_{*,\mathrm{accreted},e>0.7} = 3 \pm 1\ \mathrm{(stat.)}\pm 1\
\mathrm{(syst.)}\times10^{8}\ \mathrm{M_\odot}$, or $\sim 30-50\%$ of the
accreted halo mass. If the majority of these stars $\it{are}$ the progeny of a
massive accreted dwarf, this places an upper limit on its stellar mass, and
implies a halo mass for the progenitor of $\sim 10^{10.2\pm0.2}\
\mathrm{M_\odot}$. This constraint not only shows that the
$\it{Gaia-Enceladus}$/Sausage progenitor may not be as massive as originally
suggested, but that the majority of the Milky Way stellar halo was accreted.
These measurements are an important step towards fully reconstructing the
assembly history of the Milky Way.
