From: Rabbi Akiva Eiger
To: Unknown recipient
Rabbi Akiva Eiger systematically rejects three arguments for permitting a child under nine to carry seforim to synagogue on Shabbos without an eruv. He demonstrates that the Rashba's leniency allowing one to feed a child a rabbinic prohibition applies only for the child's own benefit, not for the adult's purposes, and that the shofar and asi l'misrach analogies likewise fail. He concludes with a practical solution: give the child the seforim for the child's own use in prayer, and the adult may accompany the child naturally.
Source: Shu"t Rabbi Akiva Eiger §15