  In order to determine the incidence of black hole accretion-driven nuclear
activity in nearby galaxies, as manifested by their radio emission, we have
carried out a high-resolution Multi-Element Radio-Linked Interferometer Network
(MERLIN) survey of LINERs and composite LINER/H{\sc ii} galaxies from a
complete magnitude-limited sample of bright nearby galaxies (Palomar sample)
with unknown arcsecond-scale radio properties. There are fifteen radio
detections, of which three are new subarcsecond-scale radio core detections,
all being candidate AGN. The detected galaxies supplement the already known
low-luminosity AGN -- low-luminosity Seyferts, LINERs and composite LINER/H{\sc
ii} galaxies -- in the Palomar sample. Combining all radio-detected Seyferts,
LINERs and composite LINER/H{\sc ii} galaxies (LTS sources), we obtain an
overall radio detection rate of 54% (22% of all bright nearby galaxies) and we
estimate that at least $\sim$50% ($\sim$20% of all bright nearby galaxies) are
true AGN. The radio powers of the LTS galaxies allow the construction of a
local radio luminosity function. By comparing the luminosity function with
those of selected moderate-redshift AGN, selected from the 2dF/NVSS survey, we
find that LTS sources naturally extend the RLF of powerful AGN down to powers
of about 10 times that of Sgr A*.
