Talk:Hausdorff dimension

"If M is a metric space, and d > 0 is a real number, then the d-dimensional Hausdorff measure Hd(M) is defined to be the infimum of all m > 0 such that for all r > 0, M can be covered by countably many closed sets of diameter < r and the sum of the d-th powers of these diameters is less than or equal to m."

I read infimium, so I'm clear on that, but this definition is still opaque to me. Please clarify. --BlackGriffen