We introduce and study in a general setting the concept of homogeneity
of an operator and, in particular, the notion of homogeneity of an
integral operator. In the latter case, homogeneous kernels of such
operators are also studied. The concept of homogeneity is associated
with transformations of a measure - measure dilations, which are most
natural in the context of our general research scheme. For the study of
integral operators, the notions of weak and strong homogeneity of the
kernel are introduced. The weak case is proved to generate a homogeneous
operator in the sense of our definition, while the stronger condition
corresponds to the most relevant specific examples - classes of
homogeneous integral operators on various metric spaces, and allows us
to obtain an explicit general form for the kernels of such operators.
The examples given in the article - various specific cases - illustrate
general statements and results given in the paper and at the same time
are of interest in their own way.