  We estimate the merger rate of double degenerate binaries containing
extremely low mass (ELM) <0.3 Msun white dwarfs in the Galaxy. Such white
dwarfs are detectable for timescales of 0.1 Gyr -- 1 Gyr in the ELM Survey; the
binaries they reside in have gravitational wave merger times of 0.001 Gyr --
100 Gyr. To explain the observed distribution requires that most ELM white
dwarf binary progenitors detach from the common envelope phase with <1 hr
orbital periods. We calculate the local space density of ELM white dwarf
binaries and estimate a merger rate of 3e-3/yr over the entire disk of the
Milky Way; the merger rate in the halo is 10 times smaller. The ELM white dwarf
binary merger rate exceeds by a factor of 40 the formation rate of stable mass
transfer AM CVn binaries, marginally exceeds the rate of underluminous
supernovae, and is identical to the formation rate of R CrB stars. On this
basis, we conclude that ELM white dwarf binaries can be the progenitors of all
observed AM CVn and possibly underluminous supernovae, however the majority of
He+CO white dwarf binaries go through unstable mass transfer and merge, e.g.
into single massive ~1 Msun white dwarfs.
