Computable Jordan Decomposition of Linear Continuous Functionals on $C[0;1]$
Computable Jordan Decomposition of Linear Continuous Functionals on $C[0;1]$
By the Riesz representation theorem using the Riemann-Stieltjes integral, linear continuous functionals on the set of continuous functions from the unit interval into the reals can either be characterized by functions of bounded variation from the unit interval into the reals, or by signed measures on the Borel-subsets. Each of …