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We show that the transverse momentum dependent transversity function isproportional to the longitudinal polarization of a quark in a transverselypolarized proton. This result suggests an alternative, convenient method fordetermining transversity, without knowing unusual fragmentation functions. Themethod consists of measuring the double spin azimuthal asymmetry insemi-inclusive pion leptoproduction by a transversely polarized proton target.The asymmetry, which is twist 3, is estimated to be more than 10% under themost favorable conditions. The experiment we suggest is feasible at facilitieslike DESY and CERN.Comment: extended version; to appear on Int. Jou. Mod. Phys.

THE TRANSVERSITY FUNCTION AND DOUBLE SPIN AZIMUTHAL ASYMMETRY IN SEMI-INCLUSIVE PION LEPTOPRODUCTION