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In the setting of metric measure spaces satisfying the doubling condition andthe $(1,p)$-Poincar\'e inequality, we prove a metric analogue of theBourgain-Brezis-Mironescu formula for functions in the Sobolev space$W^{1,p}(X,d,\nu)$, under the assumption that for $\nu$-a.e. point the tangentspace in the Gromov-Hausdorff sense is Euclidean with fixed dimension $N$.

Bourgain-Brezis-Mironescu approach in metric spaces with Euclidean tangents