A note on the Kluvánek integral

For real valued functions, Igor Kluv´anek has introduced an integral, called Archimedean, which is equivalent to the Lebesgue integral. It is based on the summation of infinite series and it avoids measure. Modifying the definition by Kluv´anek, we introduce an integral which has some good and some bad properties and we compare it with the Lebesgue integral.