Decomposition of sets of small or large boundary
Miklós Laczkovich · Mathematika · 1993
We shall say that the sets A, B xs2282 Rk are equivalent, if they are equidecomposable using translations; that is, if there are finite decompositions S0025579300007063_inline1 and vectors x1,…, xdxs2208Rk such that Bj = Aj + xj, (j = 1,…,d). We shall denote this fact by S0025579300007063_inline2 In [3], Theorem 3 we proved that if A xs2282 Rk is a bounded measurable set of positive measure then A is equivalent to a cube provided that Δ(δA)