  In the present paper, we introduce the notion of pseudo-heaviness of closed
subsets of closed symplectic manifolds and prove the existence of pseudo-heavy
fibers of moment maps. In particular, we generalize Entov and Polterovich's
theorem, which ensures the existence of non-displaceable fibers, and provide a
partial answer to a problem posed by them, which asks the existence of heavy
fibers. Moreover, we apply our results to prove that some generalized coupled
angular momenta have more than two non-displaceable fibers.
