Abstract.Following the concept of a statistically convergent sequence x , we define a statistical limit point of x as a number X that is the limit of a subsequence {xk(j)} of x such that the set {k(j): j £N} does not have density zero. Similarly, a statistical cluster point of x is a number y such that for every e > 0 the set {k € N: |x/t -y| < e} does not have density zero. These concepts, which are not equivalent, are compared to the usual concept of limit point of a sequence. Statistical analogues of limit point results are obtained. For example, if x is a bounded sequence then x has a statistical cluster point but not necessarily a statistical limit point. Also, if the set M := {k e N: xk > xk+\) has density one and x is bounded on M , then x is statistically convergent.
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