Add to ORKGLet \((X,d)\) be a metric space. We characterise the family of subsets of \(X\) on which each locally Lipschitz function defined on \(X\) is bounded, as well as the family of subsets on which each member of two different subfamilies consisting of uniformly locally Lipschitz functions is bounded. It suffices in each case to consider real-valued functions. DOI: 10.1017/S000497271400021
summary:We improve a theorem of P.G. Georgiev and N.P. Zlateva on G\^ateaux differentiability of Lip...
For a Banach space E and a compact metric space (X,d), a function F:X→E is a Lipschitz function if t...
We show that an analytic subset of the finite dimensional Euclidean space Rm is purely unrectifiable...
Let hX, di be a metric space. We characterise the family of subsets of X on which each locally Lipsc...
AbstractFor a metric space X, we study the space D∞(X) of bounded functions on X whose pointwise Lip...
Let X, d be a metric space. We find necessary and sufficient conditions on the space for the locally...
Let (X, d) be a quasi-convex, complete and separable metric space with reference probability measure...
The aim of this book is to present various facets of the theory and applications of Lipschitz functi...
The aim of this paper is to establish a compactness result on some function sets. More precisely, ou...
For a metric space X, we study the space D∞(X) of bounded functions on X whose infinitesimal Lipschi...
AbstractDavid Preiss proved that every locally Lipschitz function on an open subset of a Banach spac...
Let X atd,Ibe metric spaces with metrics d and d', respectively. A map f: X-Y is Lipschitz if t...
AbstractLet X be a compact metric space, and let V= {F(a, x): a ϵ A} where A is an open subset of Rn...
In this note we give a self-contained account of the relationship between the sequential and topolog...
For a compact metric space $K$ the space $\mathrm{Lip}(K)$ has the Daugavet property if and only if ...
summary:We improve a theorem of P.G. Georgiev and N.P. Zlateva on G\^ateaux differentiability of Lip...
For a Banach space E and a compact metric space (X,d), a function F:X→E is a Lipschitz function if t...
We show that an analytic subset of the finite dimensional Euclidean space Rm is purely unrectifiable...
Let hX, di be a metric space. We characterise the family of subsets of X on which each locally Lipsc...
AbstractFor a metric space X, we study the space D∞(X) of bounded functions on X whose pointwise Lip...
Let X, d be a metric space. We find necessary and sufficient conditions on the space for the locally...
Let (X, d) be a quasi-convex, complete and separable metric space with reference probability measure...
The aim of this book is to present various facets of the theory and applications of Lipschitz functi...
The aim of this paper is to establish a compactness result on some function sets. More precisely, ou...
For a metric space X, we study the space D∞(X) of bounded functions on X whose infinitesimal Lipschi...
AbstractDavid Preiss proved that every locally Lipschitz function on an open subset of a Banach spac...
Let X atd,Ibe metric spaces with metrics d and d', respectively. A map f: X-Y is Lipschitz if t...
AbstractLet X be a compact metric space, and let V= {F(a, x): a ϵ A} where A is an open subset of Rn...
In this note we give a self-contained account of the relationship between the sequential and topolog...
For a compact metric space $K$ the space $\mathrm{Lip}(K)$ has the Daugavet property if and only if ...
summary:We improve a theorem of P.G. Georgiev and N.P. Zlateva on G\^ateaux differentiability of Lip...
For a Banach space E and a compact metric space (X,d), a function F:X→E is a Lipschitz function if t...
We show that an analytic subset of the finite dimensional Euclidean space Rm is purely unrectifiable...