  Semiclassical contributions to the gravitational action include various terms
with zero, two, and four derivatives of the metric as well as nonlocal form
factors for these terms. Contributions to some of these terms could be confused
with others on a specific metric background or for a particular gauge fixing.
We present a critical analysis of the recent works where the tensor structure
and the number of derivatives in the action of gravity were not properly taken
into account. Taking these relevant aspects into account, we show that although
some contributions owing to the quantum fluctuations of massive or massless
scalar as well as fermion and vector fields may be attributed to the "running"
of the cosmological constant, in reality they correspond to the fourth
derivative terms of the action.
