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We continue the study (initiated in [1]) of Borel measures whose timeevolution is provided by an interacting Hamiltonian structure. Here, theprincipal focus is the development and advancement of deficency in the measurecaused by displacement of mass to infinity in finite time. We introduce - andstudy in its own right - a regularization scheme based on a dissipativemechanism which naturally degrades mass according to distance traveled (inphase space). Our principal results are obtained based on some dynamicalconsiderations in the form of a condition which forbids mass to return frominfinity.

Hamiltonian ODE's on a Space of Deficient Measures