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We prove a sum-shuffle formula for multiple zeta values in Tate algebras (inpositive characteristic), introduced in \cite{PEL3}.This follows from an analogresult for double twisted power sums, implying that an ${\mathbb{F}\_p$-vectorspace generated by multiple zeta values in Tate algebras is an${\mathbb{F}\_p$-algebra.

A sum-shuffle formula for zeta values in Tate algebras