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In this study, we employ the established Carleman estimates and propagationestimates of smallness from measurable sets for real analytic functions, alongwith the telescoping series method, to establish an observability inequalityfor the degenerate parabolic equation over measurable subsets in the time-spacedomain. As a direct application, we formulate a captivating Stackelberg-Nashgame problem and provide a proof of the existence of its equilibrium.Additionally, we characterize the set of Stackelberg-Nash equilibria and delveinto the analysis of a norm optimal control problem.

Observability Inequality from Measurable Sets and the Stackelberg-Nash Game Problem for Degenerate Parabolic Equations