Let $K$ be a compact subset of $mathbf{R}$, $mu$ be a $sigma-$finite positive measure, and $s$ an integrable function on $K$. One-sided $L^{1}$-norm is defined as |s|=max {int_{s>0}|s(x)|dmu, int_{s< 0}|s(x)|dmu}. Best simultaneous approximation of subset $S$ from a subspace $W$ (both of them are subsets of a lattice Banach space as $X$) in this norm is discussed. We give a characterization of best simultaneous approximation for a subset $S$ from subspace $W$ with One-sided $L^{1}$-norm.
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机译：假设$ K $是$ mathbf {R} $的紧凑子集，$ mu $是$ sigma- $有限正度量，$ s $是$ K $的可积函数。单面$ L ^ {1} $范数定义为 | s | = max { int_ {s> 0} | s（x）| d mu， int_ {s <0} | s（x）| d mu }。讨论了在该范数中从子空间$ W $的子集$ S $的最佳同时逼近（它们都是作为$ X $的格子Banach空间的子集）。我们给出了具有单侧$ L ^ {1} $范数的子空间$ W $中子集$ S $的最佳同时逼近的特征。
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