[...]... theorem in infinite dimensions Application: weak compactness in LJ^ Portugaliae Math 55, 113-128 (1998) 24 Sion, M.: On general minimax theorems Pacific J Math 8, 171-176 (1958) Adv Math Econ 10, 3 1 ^ 9 (2007) Advances in MATHEMATICAL ECONOMICS ©Springer 2007 Capital-labor substitution and indeterminacy in continuous-time two-sector models* Jean-Philippe Garnier^, Kazuo Nishimura^ and Alain Venditti^... mapping transforming weakly convergent sequences in G into sequences in W converging in measure with respect to the norm topology of F\ Let j be a convex normal integrand defined on[0, I] x F satisfying 0,.) is convex lower semi-continuous on E (alias convex normal integrand) and... the mapping / i-^ N\(f) is lower semicontinuous on L } „ [ F ] ( Q , JT, /X) for the topology or(L},,[F](/x), Lf(fi)) The following result deals with some convergence properties for a class of unbounded sequences in (L^p,[F](Q, T, /x), A^i) and leads to interesting apphcations in several problems of convergence of F'-valued scalarly integrable random variables, in particular, Fatou type Lemma in L\,\F\(Q.,T,... two-sector infinite-horizon growth models with sector specific external effects in production and linear preferences ^ For instance, considering Cobb-Douglas technologies, Benhabib and Nishimura [2] prove within a continuous-time model that the existence of local indeterminacy is obtained if and only if there is a reversal of factor intensities between the private and social levels The consumption * We are... convergence in measure and q(.) is upper semicontinuous on /C By virtue of Proposition 3.1, there is u e Sr such that p{u) = min p{u) ueSr As q{.) is upper semicontinuous on /C, there isveIC such that q(v) = max^(i;) veJC So we get q(v) < ^(u,v) < p{u) Other variants of Proposition 3.5 are available Compare with Proposition 8.3.3 in [13] and the results stated below The following is a min-max result involving... maxmin/(M, X) < J(u, X) < XeTlueH vmnm3xJ(u,X) ueH veU (b) max min J(u, k) = min max 7(M, k) Proof (a) follows the same line of the proof of the preceding result Nevertheless this need a careful look Let us set p(u) := max 7(M, A,), Wu eH ken and q(k) := min J(u,X), V eU A ueH For each A 6 7^ the convex integral functional , J(u, X):= \ j(t, u(t), z)kt{dz) dt is convex lower semicontinuous on 7Y, indeed,... Tightness conditions and Integrability of the sequential weak upper limit of a sequence of Multifunctions Working paper 2005 16 Castaing, C , Hess, Ch., Saadoune, M.: On various versions of Fatou lemma Working paper 2006 17 Castaing, C, Saadoune, M.: Dunford-Pettis-types theorem and convergences in set-valued integration, J Nonlinear Convex Anal 1(1), 37-71 (2000) 18 Castaing, C , Valadier, M.: Convex . seriously interested in obtaining new challenging stimuli from economic the- ories and those economists who are seeking effective mathematical tools for their research. The scope of Advances in Mathematical. 978-4-431-72733-0 Springer Tokyo Berlin Heidelberg New York Printed on acid-free paper Springer is a part of Springer Science-hBusiness Media springer.com ©Springer Japan 2007 Fainted in Japan This. Further Minimization problems and Min-Max type results involving saddle-points and Young measures are also investigated. Key words: Biting Lemma, Komlos convergence, minimization, Min-Max, saddle