  We summarise the main results obtained over the last two years by the ESO
Slice Project (ESP) redshift survey, concerning the luminosity function and
mean density of galaxies, and their implications for the galaxy number counts
at bright magnitudes. The bj-band luminosity function is characterised by a
steep faint-end, which raises above a "global" Schechter fit for M_bj > -17 +
5log(h) and is well described by a power-law with slope ~ -1.6. This steepening
is mostly produced by galaxies with emission lines, with a clear trend for
galaxies with larger [OII] equivalent widths to show a steeper faint end (and a
fainter M*). The normalization of the luminosity function is about a factor of
1.6 higher that that from the Stromlo-APM survey. We find that, in fact, the
mean density can be seen to increase out to ~140/h Mpc. If we take this into
account when computing the expected cumulative number counts from the observed
luminosity function, we are able to reproduce the observed steep counts at
bright (bj<17) magnitudes very accurately.
