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If $D$, $E$ are measurable subsets of $\\R^d$ with $E\\subseteq D$ and $|D|<\\infty$, then $$ \\int_{D\\setminus E} |T_{m}\\chi_E(x)|\\mbox{d}x\\leq \\begin{cases} |E|+|E|\\ln\\left(\\frac{|D|}{2|E|}\\right), & \\mbox{if}|E|<|D|/2, |D\\setminus E|+\\frac{1}{2}|D \\setminus E|\\ln \\left(\\frac{|E|}{|D\\setminus E|}\\right), & \\mbox{if}|E|\\geq |D|/2. \\end{cases}. $$ Here $|\\cdot|$ denotes the Lebesgue measure on $\\bR^d$. 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