  Local luminosity functions are fundamental benchmarks for high-redshift
galaxy formation and evolution studies as well as for models describing these
processes. Determining the local luminosity function in the submillimeter range
can help to better constrain in particular the bolometric luminosity density in
the local Universe, and Herschel offers the first opportunity to do so in an
unbiased way by imaging large sky areas at several submillimeter wavelengths.
  We present the first Herschel measurement of the submillimeter 0<z<0.2 local
luminosity function and infrared bolometric (8-1000 $\mu$m) local luminosity
density based on SPIRE data from the HerMES Herschel Key Program over 14.7
deg^2.
  Flux measurements in the three SPIRE channels at 250, 350 and 500 \mum are
combined with Spitzer photometry and archival data. We fit the observed
optical-to-submillimeter spectral energy distribution of SPIRE sources and use
the 1/V_{max} estimator to provide the first constraints on the monochromatic
250, 350 and 500 \mum as well as on the infrared bolometric (8-1000 \mum) local
luminosity function based on Herschel data.
  We compare our results with modeling predictions and find a slightly more
abundant local submillimeter population than predicted by a number of models.
Our measurement of the infrared bolometric (8-1000 \mum) local luminosity
function suggests a flat slope at low luminosity, and the inferred local
luminosity density, 1.31_-0.21^+0.24 x 10^8 Lsun Mpc^-3, is consistent with the
range of values reported in recent literature.
