Ordered prime divisors of a random integer (Q801109)

The author attempts to find the harmonic density of integers \(n\leq N\) whose r-th largest prime divisor does not exceed \(N^ x\), \(0\leq x\leq 1\). Ignoring that densities (harmonic or natural) are additive but not \(\sigma\)-additive, the author works on an abstract probability space in which prime divisors are independent, and from limit theorems in such a large (abstract) space the conclusion is drawn that the harmonic density of the above set exists, and these densities are identified. The result, however, may or may not have anything to do with densities in view of the oversight mentioned earlier.