  We study the escape of Ly-alpha photons from Ly-alpha emitting galaxies
(LAEs) and the overall galaxy population using a sample of 99 LAEs at 1.9<z<3.8
detected through integral-field spectroscopy of blank fields by the HETDEX
Pilot Survey. For 89 LAEs showing counterparts in deep broad-band images we
measure the rest-frame UV luminosity and the UV slope, which we use to estimate
E(B-V) under the assumption of a constant intrinsic UV slope for LAEs. These
two quantities are used to measure the dust-corrected star formation rate
(SFR). A comparison between the observed Ly-alpha luminosity and that predicted
by the dust-corrected SFR yields the Ly-alpha escape fraction. We also measure
the Ly-alpha luminosity function. Integration of the luminosity function
provides a measurement of the Ly-alpha luminosity density across our redshift
range. We combine our data with that from other surveys at 0.3<z<7.7 to trace
the evolution of the Ly-alpha luminosity density. We then compare it to that
expected from the star-formation history of the universe in order to
characterize the evolution of the Ly-alpha escape fraction of the overall
galaxy population [abriged]
