Invariant delta functions are most adequately interpreted in the sense of distributions of L. Schwartz. They are expressed as the sum of proper distributions and mass-dependent point functions. First terms are interpreted as the logarithmic or finite parts of the divergent integrals corresponding to the inverse square of the four-dimensional distance. Point function term of Δ(1) exhibits logarithmic singularities on the surface of the light cone, defining a finite value as a distribution.