The concept of statistical convergence of a sequence was first introduced by H. Fast. Statistical convergence was generalized by R. C. Buck, and studied by other authors, using a regular nonnegative summability matrix
A
A
in place of
C
1
{C_1}
. The main result in this paper is a theorem that gives meaning to the statement:
S
=
{
s
n
}
S = \{ {s_n}\}
converges to
L
L
statistically
(
T
)
(T)
if and only if "most" of the subsequences of
S
S
converge, in the ordinary sense, to
L
L
. Here
T
T
is a regular, nonnegative and triangular matrix. Corresponding results for lacunary statistical convergence, recently defined and studied by J. A. Fridy and C. Orhan, are also presented.