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Lebesgue measure and mappings of the Sobolev class W 1 , n

O. Martio (1995)

Banach Center Publications

We present a survey of the Lusin condition (N) for W 1 , n -Sobolev mappings f : G n defined in a domain G of n . Applications to the boundary behavior of conformal mappings are discussed.

Lebesgue points for Sobolev functions on metric spaces.

Juha Kinnunen, Visa Latvala (2002)

Revista Matemática Iberoamericana

Our main objective is to study the pointwise behaviour of Sobolev functions on a metric measure space. We prove that a Sobolev function has Lebesgue points outside a set of capacity zero if the measure is doubling. This result seems to be new even for the weighted Sobolev spaces on Euclidean spaces. The crucial ingredient of our argument is a maximal function related to discrete convolution approximations. In particular, we do not use the Besicovitch covering theorem, extension theorems or representation...

Les topologies sygma-Lebesgue sur C(X).

Belmesnaoui Aqzzouz, Redouane Nouira (2004)

Extracta Mathematicae

We prove that if X is a compact topological space which contains a nontrivial metrizable connected closed subset, then the vector lattice C(X) does not carry any sygma-Lebesgue topology.

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