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Assume that <math>M\ </math> is a compact locally connected Hausdorff space. The following statements hold:
¤ every size function <math>\ell_{(M,\varphi)}(x,y)</math> is a [[non-decreasing function]] in the variable <math>x\ </math> and a [[Nonincreasing function|non-increasing function]] in the variable <math>y\ </math>.
¤ every size function <math>\ell_{(M,\varphi)}(x,y)</math> is locally right-constant in both its variables.
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