  This paper continues the study of the structures induced on the ``invisible
boundary'' of the modular tower and extends some results of math.NT/0102006. We
start with a systematic formalism of pseudo-measures generalizing the
well-known theory of modular symbols for SL(2). These pseudo-measures, and the
related integral formula which we call the Levy-Mellin transform, can be
considered as an ``infinity-adic'' version of Mazur's p-adic measures
introduced in the seventies in the theory of p-adic interpolation of Mellin
transforms of cusp forms. A formalism of iterated Levy-Mellin transform in the
style of math.NT/0502576 is sketched. Finally, we discuss the invisible
boundary from the perspective of non-commutative geometry.
