  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.
