The vector lattice of norm-to-order bounded operators from C_c(X) or C_0(X) into a Dedekind complete normal vector lattice E is isomorphic to the vector lattice of E-valued regular Borel measures on X, with isometric versions under additional assumptions on E.
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Riesz representation theorems for vector lattices and Banach lattices of regular operators
The vector lattice of norm-to-order bounded operators from C_c(X) or C_0(X) into a Dedekind complete normal vector lattice E is isomorphic to the vector lattice of E-valued regular Borel measures on X, with isometric versions under additional assumptions on E.