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We prove that the decreasing rearrangement of a dyadic A1 weight w withdyadic A1 constant [w]_{1,T}=c with respect to a tree T of homogeneity k,on anon-atomic probability space, is a usual A1 weight on (0,1] with A1 constantnot more than kc-k+1.We prove also that the result is sharp, when one considersall such weights w.

Dyadic A1 weights and equimeasurable rearrangements of functions