Any Borel probability measure supported on a Cantor set included in [Formula: see text] and of zero Lebesgue measure on the real line possesses a discrete inverse measure. We study the validity of the multifractal formalism for the inverse measures of random weak Gibbs measures. The study requires, in particular, to develop in this context of random dynamics a suitable version of the results known for heterogeneous ubiquity associated with deterministic Gibbs measures.

中文翻译：

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随机弱吉布斯测度逆的多重分形形式

[公式：见正文]中包含的康托集上支持的任何 Borel 概率测度和实线上的零 Lebesgue 测度都具有离散逆测度。我们研究了多重分形形式对随机弱吉布斯测度的逆测度的有效性。该研究尤其需要在随机动力学的背景下开发出与确定性吉布斯测量相关的异构普遍性已知结果的合适版本。