Homogeneous random fractals form a probabilistic generalisation of self-similar sets with more dependencies than in random recursive constructions. Under the Uniform Strong Open Set Condition we show that the mean D-dimensional (average) Minkowski content is positive and finite, where the mean Minkowski dimension D is, in general, greater than its almost sure variant. Moreover, an integral representation extending that from the special deterministic case is derived.

中文翻译：

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均质随机分形的平均Minkowski含量

同质随机分形形成自相似集的概率泛化，比随机递归构造具有更多的依赖性。在均匀强开集条件下，我们表明平均D维（平均）Minkowski含量为正且有限，其中平均Minkowski维D通常大于其几乎确定的变量。此外，得到了从特殊确定性情况扩展出的整体表示。