  In this note a review, some considerations and new results about maps with
values in a distribution space and domain in a $\sigma$-finite measure space
$X$, are obtained. In particular, it is a survey about Bessel, frames and bases
(in particular Riesz and Gel'fand bases) in a distribution space. In this
setting, the Riesz-Fischer maps and semi-frames are defined and new results
about them are attained. Some example in tempered distributions space are
examined.
