It was proved [3] that the convergence fieldof regular matrix transformation is a very porous set in the spacethe space of all sequence of real or complex numbers while in [2 ], it was proven to be a σ-porous set in the linear metric space endowed with Fréchet metric. In [6] it was proved that is dense and close set inif and only ifis regular and porous ifis regular. Thus, this paper present a measured defined on and alongside with the conditions for their measurability.