  Kolmogorov argued that the concept of information exists also in problems
with no underlying stochastic model (as Shannon's information representation)
for instance, the information contained in an algorithm or in the genome. He
introduced a combinatorial notion of entropy and information $I(x:\sy)$
conveyed by a binary string $x$ about the unknown value of a variable $\sy$.
The current paper poses the following questions: what is the relationship
between the information conveyed by $x$ about $\sy$ to the description
complexity of $x$ ? is there a notion of cost of information ? are there limits
on how efficient $x$ conveys information ?
  To answer these questions Kolmogorov's definition is extended and a new
concept termed {\em information width} which is similar to $n$-widths in
approximation theory is introduced. Information of any input source, e.g.,
sample-based, general side-information or a hybrid of both can be evaluated by
a single common formula. An application to the space of binary functions is
considered.
