Vacuum Integration: UV- and IR-Divergencies

In this note we present the important details regarding the massless vacuum integrations which are not outlined in the literature. In particular, it has been shown how the delta-function represents either UV‑regime or IR-regime. In the case of vacuum integration, we advocate the use of sequential approach to the singular generated functions (distributions). The sequential approach is extremely useful for many practical applications, in particular, in the effective potential method.