  Weak gravitational lensing provides a unique method to directly map the dark
matter in the universe and measure cosmological parameters. Current weak
lensing surveys are limited by the atmospheric seeing from the ground and by
the small field of view of existing space telescopes. We study how a future
wide-field space telescope can measure the lensing power spectrum and skewness,
and set constraints on cosmological parameters. The lensing sensitivity was
calculated using detailed image simulations and instrumental specifications
studied in earlier papers in this series. For instance, the planned
SuperNova/Acceleration Probe (SNAP) mission will be able to measure the matter
density parameter Omega_m and the dark energy equation of state parameter w
with precisions comparable and nearly orthogonal to those derived with SNAP
from supernovae. The constraints degrade by a factor of about 2 if redshift
tomography is not used, but are little affected if the skewness only is
dropped. We also study how the constraints on these parameters depend upon the
survey geometry and define an optimal observing strategy.
