This algebra is referred to as the "Group Algebra" of "G". By the Fubini–Tonelli theorem, the convolution is submultiplicative with respect to the formula_30 norm, making formula_77 a Banach algebra. The Banach algebra formula_77 has a multiplicative identity element if and only if "G" is a discrete group, namely the function that is 1 at the identity and zero elsewhere. In general, however, it has an approximate identity which is a net (or generalized sequence) formula_81 indexed on a directed set formula_82 such that formula_83