For every compact set E in the real line with dim_A E > 0, there exist measures supported on E with any prescribed upper Assouad dimension D > dim_A E, and for any d < dim_L E, a measure with lower Assouad dimension d.
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Measures with specified support and arbitrary Assouad dimensions
For every compact set E in the real line with dim_A E > 0, there exist measures supported on E with any prescribed upper Assouad dimension D > dim_A E, and for any d < dim_L E, a measure with lower Assouad dimension d.