Search results for "First-return integral"

On the first return integrals

2007

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.