Uniqueness of the solution of the filtering equations in spaces of measures

Nonlinear filtering is a pivotal problem that has attracted significant attention from mathematicians, statisticians, engineers, and various other scientific disciplines. The solution to this problem is governed by the so-called filtering equations. In this paper, we investigate the uniqueness of solutions to these equations within measure spaces and introduce a novel, generalized framework for this analysis. Our approach provides new insights and extends the applicability of existing theories in the study of nonlinear filtering.