Resolution-limited measure and dimension (Q1200214)

If one replaces \(\varepsilon\)-covers of sets by so-called \((\varepsilon_ 0,\varepsilon)\)-covers for \(\varepsilon_ 0 < \varepsilon\), the diameters are in the interval \([\varepsilon_ 0,\varepsilon]\), then the same procedure as for ordinary Hausdorff measure leads to the so-called resolution-limited Hausdorff measure and dimension. The author's intention is to overcome the situation between theoretical dimension notions not including any limitation to the resolution, with which a set will be measured, and real world sets. The paper contains then a lot of trivial statements directly derived from simple ones for Hausdorff measures. The last section concerning illustrative examples does not contain any convincing example for this theory.