Then every Lipschitz function f from an open subset U of [R.sup.n] into Y is Gateaux differentiable off a null set of U.

Applying Lemma 7 to [X.sub.n] and N(C) [intersection] [X.sub.n], then [[phi].sub.m] are Gateaux differentiable off a null set of N(C) [intersection] [X.sub.n].

Then W is not null set in N(C) [intersection] [X.sub.n].

Although node 2 has already broadcast the message in Step I, in Step II, based on s = 1 and r = 2, yielding the result of a null set, node 2 is not required to rebroadcast the message.

Because N(1) [intersection] {N(N(i))-N(i)} is not a null set, node 1 (or N(j) where i = 1, j = 1, one of nodes among n(i)'s one-hop neighboring nodes) should be selected as one of the forward nodes, [f.sub.n] = {1}.

In the hierarchical structure of set theory, the most basic set is the null set. The null (or the empty) set has no members and it is the subset of every other subset.

Would the deans of business at these campuses agree with Cheit's null set? Possibly not.

Conversely, one could predict that executives might describe business schools which place almost no emphasis on the professional dimension as being within an alternative "null set." When business schools received most of their funding from the university, they may have been able to ignore the preferences of the business community.