Abstract:Assuming strong irreducibility and proximality, we prove that the Furstenberg measure, corresponding to a finitely supported measure on the general linear group of a finite dimensional real vector space, is exact dimensional. We also establish a Ledrappier-Young type formula for its dimension. The general strategy of the proof is based on the argument given by Feng for the exact dimensionality of self-affine measures.

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中文翻译：

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Furstenberg 度量的精确维数和 Ledrappier-Young 公式

摘要：假设强不可约性和邻近性，我们证明 Furstenberg 测度对应于有限维实向量空间的一般线性群上的有限支持测度，是精确维数。我们还为其维度建立了一个 Ledrappier-Young 型公式。证明的一般策略是基于冯给出的关于自仿射度量的确切维度的论点。

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