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- W2045781493 abstract "For a measure P defined on the $sigma $-algebra B of Borel sets of the real line with Lebesgue measure L, the concentration functions [ Q( {P,z} ) = mathop {sup }limits_{x in R} {bf P}left( {left[ {x,x + z} right)} right),qquad widehat Qleft( {P,z} right) = sup left{ {{bf P}left( A right): Lleft( A right) leq z, A in mathcal{B}} right}] and the concentration function of the decomposition $widehat P$: [begin{gathered} widehat Pleft( {left[ { - z,0} right)} right) = widehat Pleft( {left( {0,z} right]} right) = {{left( {widehat Qleft( {P,2z} right) - widehat Qleft( {P,0} right)} right)} mathord{left/ {vphantom {{left( {widehat Qleft( {P,2z} right) - widehat Qleft( {P,0} right)} right)} 2}} right. kern-nulldelimiterspace} 2},quad z > 0, hfill ,,,,,,,,, widehat Pleft( {left{ 0 right}} right) = widehat Qleft( {P,0} right) hfill end{gathered} ] are introduced. It is proved that if the finite measures $P_k $ and $T_k $ satisfy $widehat Q(P_k ,z) leq widehat Q(T_k ,z), k = 1, ldots ,n$, then $widehat Q(P_1 * cdots * P_n ,z) leq Q(widehat P_1 * cdots * widehat P_n ,z) leq Q(widehat T_1 * cdots * widehat T_n ,z)$." @default.
- W2045781493 created "2016-06-24" @default.
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- W2045781493 date "1994-09-01" @default.
- W2045781493 modified "2023-10-18" @default.
- W2045781493 title "Inequalities for Concentration of a Decomposition" @default.
- W2045781493 doi "https://doi.org/10.1137/1138057" @default.
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