We study the properties of sums of lower records from a distribution on
$[0,\infty)$ which either is continuous, except possibly
at the origin or has support contained in the set of non-negative integers.
We find necessary and sufficient condition for the partial sums of lower
records to converge almost surely to a proper random variable. Explicit
formula for the Laplace transform of the limit is derived. This limit is
infinite divisible and we show that all infinitely divisible random
variables with continuous Levy measure on $[0, \infty)$ originate as infinite
sums of lower records.