Effective bounds for convergence, descriptive complexity, and natural examples of simple and hypersimple sets

Let μ be a universal lower enumerable semi-measure (defined by L. Levin). Any computable upper bound for μ can be effectively separated from zero with a constant (this is similar to a theorem of G. Marandzhyan).Computable positive lower bounds for μ can be nontrivial and allow one to construct natural examples of hypersimple sets (introduced by E. Post).