The Mackey Continuity of the Monotone Rearrangement

Anthony Horsley, Andrzej J. Wrobel
1986 Proceedings of the American Mathematical Society  
Let (A, A,ß) be a probability space, and let mes denote the Lebesgue measure on the Borel cr-algebra B in [0,1). The nondecreasingrearrangement operator from the space L°°(ß) = L°°(A,A,p) of real-valued essentially bounded functions into L°° -L°°([0,1], S,mes) is shown to be uniformly continuous in the Mackey topologies T(L°°(ß),L1(p)) and t(L°°,L1) on L°°(ß) and L°°, respectively.
doi:10.2307/2045917 fatcat:o3m7fzbnnfcappuamggwunjwre