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Let (M, ω) be a Hamiltonian G-space with proper momentum map J : M → g * . It is well-known that if zero is a regular value of J and G acts freely on the level set J −1 (0), then the reduced space M 0 := J −1 (0)/G is a symplectic manifold. We show that if the regularity assumptions are dropped the space M 0 is a union of symplectic manifolds, i.e., it is a stratified symplectic space. Arms et al.,  , proved that M 0 possesses a natural Poisson bracket. Using their result we studydoi:10.2307/2944350 fatcat:abflpeugmzfjhk5hi5xh2fup6m