07 - Tangent Measures, I

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Week 7: Tangent Measures, Part I Tangent Measures are measures generated by zooming in on the support of a measure. Their appeal is that sometimes properties that hold a.e. for a measure improve or hold uniformly for their tangent measures. To demonstrate their versatility, we prove Marstrand?s Theorem, which says any measure whose s-dimensional densities exist must have s an integer.