On the existence of solutions to the Orlicz Aleksandrov problem

In [Int Math Res Not 7: 5492–5519 (2021)], Feng and He introduced the Orlicz Aleksandrov problem and proved that, there exists a convex body and an explicit constant, such that the problem is solved provided the given measure is even. In this paper, extending their results, we first prove that the desired convex body always exists for each constant in an interval. Then, we prove the existence of solutions to the problem for general measure that is not necessarily even.