Summary: Let \(\Gamma_ X(\upsilon)=<X,A(X),\upsilon >\) be a cooperative von Neumann game with side pagments, where X is a nonempty set of arbitrary cardinality, A(X) the Boolean ring generated from P(X) with the operations \(\Delta\) and \(\cap\) for addition and multiplication, respectively, such that \(S^ 2=S\) for all \(S\in A(X)\), and \(\upsilon\) : A(X)\(\to {\mathbb{R}}_+\) with \(\upsilon (\emptyset)=0\). The Shapley- Bondareva-Schmeidler Theorem, which states that a game of the form \(\Gamma_ X(\upsilon)=<X,A(X),\upsilon >\) is weak if and only if the core of \(\Gamma_ X(\upsilon)\), \(\zeta (\Gamma_ X(\upsilon))\), is normal, may be regarded as the fundamental theorem for weak cooperative games with side-payments. In this paper we use an ultrapower construction on the reals, \({\mathbb{R}}\), to summarize a common mathematical theme employed in various constructions used to establish the Shapley- Bondareva-Schmeidler Theorem in the literature [see F. Delbaen, J. Math. Anal. Appl. 45, 210-233 (1974; Zbl 0337.90084); Y. Kannai, ibid. 27, 227-240 (1969; Zbl 0181.469); D. Schmeidler, ibid. 40, 214-225 (1972; Zbl 0243.90071); “On balanced games with infinitely many players”, Unpubl. Mauscr., The Hebrew Univ. 1967]. This common mathematical theme is that the space L, comprised of finite, real linear combinations of the collection of functions, \(\{\chi_ a: a\in A(X)\}\), possesses a certain extension property that is intimately related to the Hahn-Banach Theorem of functional analysis. A close inspection of the extension property reveals that the Shapley-Bondareva-Schmeidler Theorem is in fact equivalent to the Hahn-Banach Theorem.