F(x) = f(a) + | f,(t) dt, xe[a, b]. (a.35) the function f' in (a.35) is called the radon-nikodým derivative of f. it is uniquely measure on [a, b]. where with respect to lebesgu proposition a.34 (product rule) suppose that f, g e r(u) are absolutely continuous with radon-nikodým derivatives f',g'. then the product fg is absolutely continuous with radon-nikodým derivative f'g + fg'