Jørgensen's inequality is a result in the field of functional analysis, particularly concerning the relationships between norms in Banach spaces. Specifically, Jørgensen's inequality pertains to the estimates of certain linear operators and is often discussed in the context of submartingales, Brownian motion, and processes in probability theory.
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For a non-elementary discrete subgroup generated by , the displayed inequality is a necessary trace constraint. Failure of it proves nondiscreteness when non-elementarity has independently been checked. It is not a sufficient condition for discreteness and must not be applied to an elementary pair without its hypothesis.