  We consider the $k$-user successive refinement problem with causal decoder
side information and derive an exponential strong converse theorem. The
rate-distortion region for the problem can be derived as a straightforward
extension of the two-user case by Maor and Merhav (2008). We show that for any
rate-distortion tuple outside the rate-distortion region of the $k$-user
successive refinement problem with causal decoder side information, the joint
excess-distortion probability approaches one exponentially fast. Our proof
follows by judiciously adapting the recently proposed strong converse technique
by Oohama using the information spectrum method, the variational form of the
rate-distortion region and H\"older's inequality. The lossy source coding
problem with causal decoder side information considered by El Gamal and
Weissman is a special case ($k=1$) of the current problem. Therefore, the
exponential strong converse theorem for the El Gamal and Weissman problem
follows as a corollary of our result.
