For an arbitrary self-affine measure defined by a self-affine iterated function system and a family of probability weights, it is proven in this article that, if a self-affine measure is a spectral measure, then the probability weights must be equal and measure non-overlap holds in a weaker sense. In particular, all spectral integral self-affine measures satisfy the OSC.

中文翻译：

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光谱自仿射测度的均匀性

对于由自仿射迭代函数系统和一系列概率权重定义的任意自仿射测度，本文证明，如果自仿射测度是频谱测度，则概率权重必须相等，并且在较弱的意义上衡量非重叠保持。特别地，所有频谱积分自仿射度量都满足OSC。