By Gérard Debreu (auth.), Shigeo Kusuoka, Toru Maruyama (eds.)

ISBN-10: 4431658955

ISBN-13: 9784431658955

ISBN-10: 4431658971

ISBN-13: 9784431658979

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**Additional resources for Advances in Mathematical Economics**

**Example text**

Let (fn) be a sequence in 1i. By (5) there exists a subsequence (fnk) of (fn) such that (f::;)k converges a(L1,LOO) in L3c(p,). 1 (5)===>(6) follows immediately. (6) ===> (1) Let us apply the notations in (6). Since (Unk) converges a(L 1 , LOO) in L3c (p,), there is a sequence (um) of the form Um = L~;m Aiun, with Ai 2': 0, L~:'m Ai = 1 such that (Um) converges strongly in L3c (p,). e in X and so is the sequence (L~;:;'p A;"P fn, )p. 2. Let X be a Eanach space and H a bounded subset of L3c(p,).

1 and w. 2 are convex and closed in measure, 1 E Fatou's lemma we get w. 1 m::; 111 - 9111::; liminfllJ" - 9nlll = m. n and 9 E w. 2 . By o Convergences in L 6. L) Now we proceed to the characterizations of several modes of convergences from a bounded subset in L\(ll) via weak compactness of the truncated sequences. 1. Let X be a Banach space and H a bounded sub set of L~(tJ,). e in X. e H has the WTP). (3) Given any sequence (fn) in H, there exists a subsequence (gn) of(fn) such that (l{llh nll

Thus, the strong firm exhibits counterintuitive behavior. 2 for the same purpose, 48 E. Dierker, H. Dierker profits, deeline, if the degrce of product differentiation increases from 1/15 to 1/14. 7794. On the other hand, computing the equilibrium values of PI we found no conspicuous results. Thus we are led to ask: a) Why is it the strong rather than the weak firm that exhibits counterintuitive behavior? b) Why is the behavior of the strong firm reversed if t gets larger than some critical value (around 1/14 in this example)?

### Advances in Mathematical Economics by Gérard Debreu (auth.), Shigeo Kusuoka, Toru Maruyama (eds.)

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