Measures of affinity of a sequence for a number

We define strong and weak affinities of a number a for a sequence (x_k ) denoted by L (a,(x_k )) and U (a, (x_k )) respectively. We show U (a,(x_k )) > 0 if and only if the number a is a statistical limit point of the sequence (x_k ). We consider the distribution of sequences with positive weak and strong measures of affinity within the space l ^∞ of bounded sequences. The main result is that the set of bounded sequences with U (a,(x_k )) > 0, that is, the set of sequences with statistical limit points, is a dense subset in l ^∞ of the first category. We also show the set of sequences with positive strong affinities is a nowhere dense subset of l ^∞.