By the convexity (resp. concavity) and constant preserving condition, one can easily obtain Proposition 2.1, which shows that (S^{mathrm{cv}}) (resp. (S^{mathrm{conca}})) has minimal members (resp. maximal members).
Zorn's Lemma may then be equivalently restated as the assertion that any nonempty strongly inductive collection \(\sH\) of sets has a maximal member, that is, a member properly included in no member of \(\sH\).
Then the empty set Ø, being the union of the empty chain, is in S. If it is not a maximal member, then some other member that includes it is chosen.
Because S is a set (and not a proper class like the class of ordinal numbers), this construction ultimately must stop with a maximal member of S.
(mathcal{E}_{0} ) is a maximal member of S; (mathcal{E}_{0} ) is a linear expectation.
Then the following two statements are equivalent: (i) (mathcal{E}_{0} ) is a maximal member of S; (ii) (mathcal{E}_{0} ) is a linear expectation. .
We call (mathcal{E}_{0}) a maximal member of S if (mathcal{E}_{0}in S) and (mathcal{E}_{0}) satisfy: (A8) for any (mathcal{E}in S), if (mathcal{E} [X]geqmathcal{E}_{0} [X]), (forall Xin L^{1}mathcalOmega,mathcal{F},P)), then (mathcal{E}= mathcal{E}_{0}). .
If now a sequence X is a member of many maximal cliques, it should be assigned to that clique C i whose shared sequence part I c (C i ) overlaps X best, i.e. is maximal.
EGF exposure resulted in an increase in tyrosine phosphorylation (activation) in all ErbB receptor family members (ErbB1-4), with maximal phosphorylation observed 10 min after EGF exposure followed by a subsequent decrease in ErbB1-4 receptyrosinesine phosphorylation, reflecting the internalization and degradation of ErbB1-4 hetereceptorrecomplexesmplexes following EGF-induced activation.
35 involved team members (nurses and physicians including paediatricians, paediatric surgeons and paediatric intensivists) answered the TeamMonitor questionnaire regarding team performance (mean 4.4 members/event; minimal 2, maximal 6 members).
