Quantization of Cantor-Like Set on the Real Projective Line

In this article, an iterated function system (IFS) is considered on the real projective line RP¹ so that the attractor is a Cantor-like set. Hausdorff dimension of this attractor is estimated. The existence of a probability measure associated with this IFS on RP¹ is also demonstrated. It is shown that the n-th quantization error of order r for the push-forward measure is a constant multiple of the n-th quantization error of order r of the original measure. Finally, an upper bound for the n-th quantization error of order 2 for this measure is provided.