  (Abridged) Several aspects of the evolution of star-forming galaxies are
studied using measures of the 2-dimensional surface brightness profile of a
sample of 341 faint objects selected from the CFRS and LDSS redshift surveys
that have been observed with the Hubble Space Telescope. The size function of
disk scale lengths in disk-dominated galaxies is found to stay roughly constant
to z=1. This result, which is strengthened by inclusion of the local de Jong et
al (1996) size function, suggests that the scale lengths of typical disks can
not have grown substantially with cosmic epoch since z=1, unless a
corresponding number of large disks have been destroyed through merging. In
addition to a roughly constant number density, the galaxies with large disks
have, as a set, properties consistent with the idea that they are similar
galaxies observed at different cosmic epochs. However, on average, they show
higher B-band disk surface brightnesses, bluer overall (U-V) colors, higher
[OII] 3727 equivalent widths and less regular morphologies at high redshift
than at low redshift, suggesting an increase in the star-formation rate by a
factor of about 3 to z=0.7. This is consistent with the expectations of recent
models for the evolution of the disk of the Milky Way and similar galaxies. The
evolution of the large disk galaxies is probably not sufficient to account for
the evolution of the overall luminosity function of galaxies over the interval
0<z<1, especially if Omega=1. Analysis of the half-light radii of all the
galaxies in the sample and construction of the bivariate size-luminosity
function suggests that larger changes in the galaxy population are due to
smaller galaxies, those with half-light radii around 5 h_{50}^{-1} kpc
