The abstract absolutely continuous functions with values in locally convex spaces
Wu, Congxin; Xue, Xiaoping;
The abstract absolutely continuous functions with values in locally convex spaces
The authors define three kinds of absolute continuity for vector-valued functions mapping [0,1] into a metrizable locally convex space \(X\) (all three definitions coincide when \(X\) is finite dimensional). Then conditions on \(X\) are given so that two of the three definitions are equivalent.
Spaces of vector- and operator-valued functions, absolute continuity for vector-valued functions
Spaces of vector- and operator-valued functions, absolute continuity for vector-valued functions