Some pathological properties of the first-return integrals are explored. In particular it is proved that there exist Riemann improper integrable functions which are first-return recoverable almost everywhere, but not first-return integrable, with respect to each trajectory. It is also proved that the usual convergence theorems fail to be true for the first-return integrals.

Bongiorno, B. (2007). Remarks on the first return integral.

Remarks on the first return integral

BONGIORNO, Benedetto
2007-01-01

Abstract

Some pathological properties of the first-return integrals are explored. In particular it is proved that there exist Riemann improper integrable functions which are first-return recoverable almost everywhere, but not first-return integrable, with respect to each trajectory. It is also proved that the usual convergence theorems fail to be true for the first-return integrals.
Bongiorno, B. (2007). Remarks on the first return integral.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/46247
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