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Conditional calculus on fractal structures and its application to galaxy distribution
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Conditional calculus on fractal structures and its application to galaxy distribution
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It is shown that calculus can apply on a fractal structure with the condition that the infinitesimal limit of change of the variable is larger than the lower cut-off of the fractal structure, and an assumption called local decomposability. As an application, it is shown that the angular projection of a fractal distribution in 3-dimensional space is not homogeneous at sufficiently large angles. Therefore the angular projection of galaxy distribution for sufficiently large angles can discriminate the fractal and the homogeneity pictures.
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