On the first return integrals

Benedetto Bongiorno

On the first return integrals

Benedetto Bongiorno

Matematica e Informatica

Risultato della ricerca: Article

3 Citazioni (Scopus)

Abstract

Some pathological properties of the first-return integrals are explored. In particular it is proved that thereexist Riemann improper integrable functions which are first-return recoverable almost everywhere, but notfirst-return integrable, with respect to each trajectory. It is also proved that the usual convergence theoremsfail to be true for the first-return integrals.

Lingua originale	English
pagine (da-a)	112-116
Numero di pagine	4
Rivista	Journal of Mathematical Analysis and Applications
Volume	333
Stato di pubblicazione	Published - 2007

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All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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Bongiorno, B. (2007). On the first return integrals. Journal of Mathematical Analysis and Applications, 333, 112-116.

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PY - 2007

Y1 - 2007

N2 - Some pathological properties of the first-return integrals are explored. In particular it is proved that thereexist Riemann improper integrable functions which are first-return recoverable almost everywhere, but notfirst-return integrable, with respect to each trajectory. It is also proved that the usual convergence theoremsfail to be true for the first-return integrals.

AB - Some pathological properties of the first-return integrals are explored. In particular it is proved that thereexist Riemann improper integrable functions which are first-return recoverable almost everywhere, but notfirst-return integrable, with respect to each trajectory. It is also proved that the usual convergence theoremsfail to be true for the first-return integrals.

KW - First-return integrals

KW - First-return recovery

KW - First-return integrals

KW - First-return recovery

UR - http://hdl.handle.net/10447/40007

M3 - Article

VL - 333

SP - 112

EP - 116

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

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