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- W2009002026 abstract "Let Ω denote the unit n-cube, [0, 1]n, and let M be the set of all real valued functions on Ω which are nondecreasing in each variable. If f is a bounded Lebesgue measurable function on Ω and 1 < p < ∞, let ƒp denote the best Lp-approximation to ƒ by elements of M. It is shown that ƒp converges almost everywhere as p decreases to one to a best L1-approximation to f by elements of M. If ƒ is continuous, then ƒp is continuous and converges uniformly as p ↓ 1 to a best L1-approximation to ƒ by elements of M and ƒp converges uniformly as p → ∞ to a best L∞-approximation to ƒ by elements of M." @default.
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- W2009002026 date "1986-07-01" @default.
- W2009002026 modified "2023-10-16" @default.
- W2009002026 title "Monotone approximation in several variables" @default.
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- W2009002026 doi "https://doi.org/10.1016/0021-9045(86)90030-4" @default.
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