From: Rabbi Akiva Eiger
To: Unknown recipient
Rabbi Akiva Eiger responds to a Gaon's counter-arguments about a woman suspected of improper conduct and whether her offspring may marry into the congregation. He disputes most of the correspondent's theoretical arguments regarding kiur, kesubah forfeiture, and witness disqualification, but ultimately constructs a mamah nafshach argument using sfek sfeika combined with the mother's chazakah to permit the offspring, agreeing with the correspondent's practical conclusion where non-Jews form a majority in the city.
Source: Shu"t Rabbi Akiva Eiger §103