A probability on a heuristic sub set of integers that it is a metric space

摘要

In this work we will answer to the question, is there a probability space on a set such that it is a metric space? For answer to the question, we prove that the probability that two random positive integers given from a heuristic set defined in this article are relatively prime, is a metric space. Hence, there is a probability that it is a metric. Also, we show that this probability space is a paracompact space.