<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></abstract>

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.

A note on the Kluvánek integral

Faculty of sciences Matej Bel University Tajovsk´eho 40 SK–97-401 Bansk´a Bystrica SLOVAKIA

Institute of Mathematics Slovak Academy of Sciences ˇStef´anikova 49 SK-814 73 Bratislava SLOVAKIA

Department of Mathematics Faculty of Education Catholic University in Ruˇzomberok Hrabovsk´a cesta 1 SK–034-01 Ruˇzomberok SLOVAKIA

Tatra Mountains Mathematical Publications

{"article-title":"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...

A note on the Kluvánek integral

Published Online: Nov 13, 2012

Page range: 59 - 65

DOI: https://doi.org/10.2478/v10127-011-0024-2

Keywords
Lebesgue integral, Archimedean integral, summation of infinite series.

This content is open access.

A note on the Kluvánek integral

Published Online: Nov 13, 2012

Page range: 59 - 65

DOI: https://doi.org/10.2478/v10127-011-0024-2

KeywordsLebesgue integral, Archimedean integral, summation of infinite series.

This content is open access.

Keywords
Lebesgue integral, Archimedean integral, summation of infinite series.