In earlier papers we have developed an algebraic theory of discrete
tomography. In those papers the structure of the functions f:Aβ{0,1}
and f:AβZ having given line sums in certain directions have
been analyzed. Here A was a block in Zn with sides parallel to
the axes. In the present paper we assume that there is noise in the
measurements and (only) that A is an arbitrary or convex finite set in
Zn. We derive generalizations of earlier results. Furthermore we
apply a method of Beck and Fiala to obtain results of he following type: if the
line sums in k directions of a function h:Aβ[0,1] are known, then
there exists a function f:Aβ{0,1} such that its line sums differ by at
most k from the corresponding line sums of h.Comment: 16 page