Simultaneous Lipschitz extensions

Brudnyi, Alexander; Brudnyi, Yuri

doi:10.1070/rm2005v060n06abeh004281

Russ. Math. Surv.

2005

DOI: 10.1070/rm2005v060n06abeh004281

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Simultaneous Lipschitz extensions

Alexander Brudnyi¹,

Yuri Brudnyi²

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2008

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Linear and nonlinear extensions of Lipschitz functions from subsets of metric spaces

Brudnyi

2008

St. Petersburg Math. J.

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In case B = R, we denote the corresponding space by Lip(M ). Regarding a subset S ⊂ M as the metric space equipped with the induced metric, we introduce the family of spaces Lip(S, B). We say that M satisfies the linear Lipschitz extension property if λ(M ) < ∞.In the same way we define the nonlinear Lipschitz extension constant ν(S, M, B) to be the infimum of the constants C such that every f ∈ Lip(S, B) admits an extension toWe are ready to present the main result of the paper. For its formulation we let B fin denote the category of all finite-dimensional Banach spaces. Also, we set ν(M ) := sup{ν(M, B) : B ∈ B fin }.2000 Mathematics Subject Classification. Primary 54E40.

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Linear and nonlinear extensions of Lipschitz functions from subsets of metric spaces

Brudnyi

2008

St. Petersburg Math. J.

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Simultaneous Lipschitz extensions

Cited by 1 publication

References 18 publications

Linear and nonlinear extensions of Lipschitz functions from subsets of metric spaces

Linear and nonlinear extensions of Lipschitz functions from subsets of metric spaces

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