=+Let A be a real linear functional on a vector lattice / of (finite) real functions on a space 22. This means that if f and g lie in , then so do f V g and f Ag (with values max( f(w), g(w)} and min( f(w), g(w))), as well as af + Bg, and A(af+Bg) =@A

(f) +BA(g). Assume further of / that f ./ implies fA1€_/ (where 1 denotes the function identically equal to 1). Assume further of A that it is positive in the sense that f ≥ 0 (pointwise) implies A

(f) ≥ 0 and continuous from above at 0 in the sense that f ,, 1 0 (pointwise) implies A(f ,, ) -+ 0.