  We consider transferable utility cooperative games with infinitely many
players. In particular, we generalize the notions of core and balancedness, and
also the Bondareva-Shapley Theorem for infinite TU-games with and without
restricted cooperation, to the cases where the core consists of
$\kappa$-additive set functions.
  Our generalized Bondareva-Shapley Theorem extends previous results by
Bondareva (1963), Shapley (1967), Schmeidler (1967), Faigle (1989), Kannai
(1969), Kannai (1992), Pinter(2011) and Bartl and Pint\'er (2022).
