  Given a complex meromorphic function, it is well defined its Riesz measure in
terms of the laplacian of the logarithm of its modulus. Moreover, related to
this tool, it is possible to prove the celebrated Jensen formula. In the
present paper, using among the other things the fundamental solution for the
bilaplacian, we introduce a possible generalization of these two concepts in
the space of quaternions, obtaining new interesting Riesz measures and global
(i.e. four dimensional), Jensen formulas.
