  The main objective of the present paper is to establish a new uncertainty
principle (UP) for the two-sided quaternion Fourier transform (QFT). This
result is an extension of a result of Benedicks, Amrein and Berthier, which
states that a nonzero function in $L^1\left({\mathbb{R}}^2,
{\mathbb{H}}\right)$ and its two-sided QFT cannot both have support of finite
measure.
