@article{Racca_2019, title={Darboux Approach to Mα-integration}, volume={7}, url={https://jurnal.unai.edu/index.php/isc/article/view/1069}, DOI={10.35974/isc.v7i1.1069}, abstractNote={<p>It is known that one can develop Riemann integration theory via Darboux approach. The<br>main idea in the Darboux approach is to define an integral using upper and lower Riemann<br>sums. In this study we look at how -integration can be develop via Darboux approach.<br>Here is a brief discussion of the methodology. We define an equivalence relation on the set of<br>-divisions of , - such that for - divisions *(, - )+ and *(, - )+ we<br>say that if and only if the intervals in are exactly the intervals in . Given a<br>gauge on , - and a -fine division *(, - )+ of , -, we set<br>, - * +</p> <p>Given a function on , -, and a -fine - division , we define the upper and lower<br>sums (respectively) in the following manner<br>( ) , -( ) ( )( ) and</p> <p>( ) , -( ) ( )( )<br>provided these values exists. We were able to show that a function on , - is -<br>ntegrable if and only if the following exists and are equal:<br>(<br>) ∫<br>̅̅̅̅̅</p> <p>( ) and (<br>) ∫</p> <p>( )</p> <p>In this approach we were able to prove the basic properties of the -integral. It is our next<br>goal to extend -integration to other spaces via Darboux approach.</p>}, number={1}, journal={Abstract Proceedings International Scholars Conference}, author={Racca, Abraham P.}, year={2019}, month={Dec.}, pages={1871-1878} }