  A formal definition of epsilon-complexity of an individual continuous
function defined on a unit cube is proposed. This definition is consistent with
the Kolmogorov's idea of the complexity of an object. A definition of
epsilon-complexity for a class of continuous functions with a given modulus of
continuity is also proposed. Additionally, an explicit formula for the
epsilon-complexity of a functional class is obtained. As a consequence, the
paper finds that the epsilon-complexity for the Holder class of functions can
be characterized by a pair of real numbers. Based on these results the papers
formulates a conjecture concerning the epsilon-complexity of an individual
function from the Holder class. We also propose a conjecture about
characterization of epsilon-complexity of a function from the Holder class
given on a discrete grid.
