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This article demonstrates that the BFKL and CCFM equations, despite theirdifferent physical content, lead to equivalent results for any final-stateobservable at leading single-logarithmic order. A novel and fundamental elementis the treatment also of the soft (z->1 divergent) part of the splittingfunction in the CCFM equation.Comment: 18 pages, 7 figures. Version 2 contains a few extra sentences to  emphasise that the equivalence applies to the predictions from the equation

Soft emissions and the equivalence of BFKL and CCFM final states