  In this study, we employ the established Carleman estimates and propagation
estimates of smallness from measurable sets for real analytic functions, along
with the telescoping series method, to establish an observability inequality
for the degenerate parabolic equation over measurable subsets in the time-space
domain. As a direct application, we formulate a captivating Stackelberg-Nash
game problem and provide a proof of the existence of its equilibrium.
Additionally, we characterize the set of Stackelberg-Nash equilibria and delve
into the analysis of a norm optimal control problem.
