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In this paper we formulate and prove a theorem, which provides theconserved quantities of a system described by the generalized variational principle of Herglotz.This new theorem contains as a special case the classical first Noether theorem.It reduces to it when the generalized variational principle of Herglotz reducesto the classical variational principle.Several examples for applications to physics are given.

First Noether-type theorem for the generalized variational principle of Herglotz