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The study of harmonic analysis in superspace led to the Howe dual pair (O(m)×Sp(2n),sl2). This Howe dual pair is incomplete, which has several implications. These problems can be solved by introducing the orthosymplectic Lie supergroup OSp(m|2n). We introduce Lie supergroups in the supermanifold setting and show that everything is captured in the Harish-Chandra pair. We show the uniqueness of the supersphere integration as an orthosymplectically invariant linear functional. Finally we study the osp(m|2n)-representations of supersymmetric tensors for the natural module for osp(m|2n). [ABSTRACT FROM AUTHOR]