two properties of cousin functors

let r be a commutative noetherian ring with non-zero identity and f a filtration of spec(r). we show that the cousin functor with respect to f, cr(f, −) : c (r) −→ comp(r), where c (r) is the category of r-modules fwhich are admitted by f andf comp(r) is the category of complexes of r-modules, commutes with the formation of direct limits and is right exact. we observe that an r-module x is balanced big cohen-macaulay if (r, m) is a local ring, mx ì¸= x, and every finitely generated submodule of x is a big cohen-macaulay r-module with respect to some system of parameters for r