In this paper, we investigate the relationship between sampling measure
μ
\mu
, Berezin transform
μ
~
\tilde {\mu }
and
r
r
-averaging transform
μ
^
r
\widehat {\mu }_r
on Bergman spaces. Compared with some results of Luecking [Amer. J. Math. 107 (1985), pp. 85–111], our results provide an equivalent description of sampling measures, which reveals the reason why
1
/
μ
^
r
∈
L
∞
1/\hat {\mu }_r\in L^\infty
or
1
/
μ
~
∈
L
∞
1/\tilde {\mu }\in L^\infty
does not make sure that
μ
\mu
is a sampling measure on Bergman spaces.