  In the successive refinement problem, a fixed-length sequence emitted from an
information source is encoded into two codewords by two encoders in order to
give two reconstructions of the sequence. One of two reconstructions is
obtained by one of two codewords, and the other reconstruction is obtained by
all two codewords. For this coding problem, we give non-asymptotic inner and
outer bounds on pairs of numbers of codewords of two encoders such that each
probability that a distortion exceeds a given distortion level is less than a
given probability level. We also give a general formula for the rate-distortion
region for general sources, where the rate-distortion region is the set of rate
pairs of two encoders such that each maximum value of possible distortions is
less than a given distortion level.
