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In this work, we develop a technique to decompose a function $f\\in L^1(\\Omega)$, with vanishing mean value, into the sum of a collection of functions $\\{f_t-\\tilde{f}_t\\}_{t\\in\\Gamma}$ subordinated to $\\{\\Omega_t\\}_{t\\in\\Gamma}$ such that $Supp\\,(f_t-\\tilde{f}_t)\\subset\\Omega_t$ and $\\int f_t-\\tilde{f}_t=0$. 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