An inductive limit topology on the Denjoy space

In the early twentieth century, Denjoy and Perron independently created an integral generalizing that of Lebesgue. However, their integral has one major drawback: its definition is complicated. In the an integral that is equivalent to Denjoy's and Perron's, but whose definition is much less complicated. They defined their integral by slightly modifying one of the customary definitions of the Riemann integral; their δ is a positive function instead of a positive constant.; Let $KH$[a, b] = {lcub}f : [ a, b] → $R$ | f is Kurzweil-Henstock integrable{rcub}. Some of the research concerning Kurzweil-Henstock integration has centered on determining a topology on $KH$[a, b] that naturally reflects the properties of the integral. The most widely investigated one is that given by the Alexiewicz norm f A=supx∈ a,b a