  This lecture notes are intended for the students taking courses in
mathematical control theory. They are concerned with the attainability problem
with constraints. The exposition is oriented to the linear control problems
with the impulse constraints and the possible discontinuity in the coefficients
under control actions. In addition, the weakening of constraints is assumed.
The ordinary attainable set is replaced with the attraction set. To construct
this attraction set we realize the extension procedure; the generalized
elements are defined as finitely additive measures with the property of the
weak absolute continuity with respect to the restriction of the Lebesgue
measure. The auxiliary constructions of general topology and measure theory are
used.
