We focus on a very general problem in the theory of dynamic systems, namely that of studying measure differential inclusions with varying measures. The multifunction on the right hand side has compact non-necessarily convex values in a real Euclidean space and satisfies bounded variation hypotheses with respect to the Pompeiu excess (and not to the Hausdorff-Pompeiu distance, as usually in literature). This is possible due to the use of interesting selection principles for excess bounded variation set-valued mappings. Conditions for the minimization of a generic functional with respect to a family of measures generated by equiregulated left-continuous, nondecreasing functions and to associated solutions of the differential inclusion driven by these measures are deduced, under constraints only on the initial point of the trajectory.

我们关注动态系统理论中的一个非常普遍的问题，即研究具有不同度量的度量微分包含问题。右侧的多功能在实际的欧几里得空间中具有紧凑的不必要的凸值，并且满足关于庞贝过剩（而不是文献中通常所说的Hausdorff-Pompeiu距离）的有界变化假设。由于对多余的有界变化集值映射使用了有趣的选择原则，因此这是可能的。在仅对轨迹的起始点进行约束的情况下，推导了针对由均衡调节的左连续非递减函数生成的一系列度量以及由这些度量驱动的微分包含的相关解的最小化通用条件。