A note on the dimensions of Assouad and Aikawa

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A framework for fractional Hardy inequalities (2013, background): “Therein (T) with β = 0 is formulated in terms of a certain Aikawa dimension which equals to the upper Assouad dimension in Euclidean spaces, see [25].”
Assouad Dimension and Fractal Geometry (2020, background): “In [188] it is established that (for subsets of Euclidean space) the Assouad and Aikawa dimensions coincide, see [2].”
Muckenhoupt Ap-properties of Distance Functions and Applications to Hardy–Sobolev -type Inequalities (2017, background): “Notice that in [24] the relevant radii are always bounded from above by diam(E), whereas presently the upper bound for radii is 2 diam(X) both in the definition of co dimA and in the above Aikawa condition (11).”