  The Shannon lower bound is one of the few lower bounds on the rate-distortion
function that holds for a large class of sources. In this paper, it is
demonstrated that its gap to the rate-distortion function vanishes as the
allowed distortion tends to zero for all sources having a finite differential
entropy and whose integer part is finite. Conversely, it is demonstrated that
if the integer part of the source has an infinite entropy, then its
rate-distortion function is infinite for every finite distortion. Consequently,
the Shannon lower bound provides an asymptotically tight bound on the
rate-distortion function if, and only if, the integer part of the source has a
finite entropy.
