For real valued functions, Igor Kluvánek has introduced an integral, called Archimedean,which is equivalent to the Lebesgue integral. It is based on the summationof infinite series and it avoids measure. Modifying the definition by Kluvánek, weintroduce an integral which has some good and some bad properties and we compareit with the Lebesgue integral.
@article{113, title = {A note on the Kluv\'anek Integral}, journal = {Tatra Mountains Mathematical Publications}, volume = {49}, year = {2011}, doi = {10.2478/tatra.v49i0.113}, language = {EN}, url = {http://dml.mathdoc.fr/item/113} }
Riečan, Beloslav; Tkačik, Štefan. A note on the Kluvánek Integral. Tatra Mountains Mathematical Publications, Tome 49 (2011) . doi : 10.2478/tatra.v49i0.113. http://gdmltest.u-ga.fr/item/113/