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In this paper we obtain a new family of identities for random measures on theunit ball of a separable Hilbert space which arise as the asymptotic analoguesof the Gibbs measures in the Sherrington-Kirkpatrick and $p$-spin models andwhich are known to satisfy the Ghirlanda-Guerra identities. We give severalapplications of the new identities to structural results for such measures.

A new representation of the Ghirlanda-Guerra identities with applications