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We study generalized products of divergence-measure fields and gradientmeasures of {\rm BV} functions. These products depend on the choice of arepresentative of the {\rm BV} function, and here we single out a specificchoice which is suitable in order to define and investigate a notion of weaksupersolutions for the $1$-Laplace operator.

An Anzellotti type pairing for divergence-measure fields and a notion of weakly super-$1$-harmonic functions