By Takuji Arai (auth.), S. Kusuoka, A. Yamazaki (eds.)

ISBN-10: 4431777830

ISBN-13: 9784431777830

ISBN-10: 4431777849

ISBN-13: 9784431777847

A lot of monetary difficulties can formulated as limited optimizations and equilibration in their ideas. a variety of mathematical theories were providing economists with critical machineries for those difficulties bobbing up in financial idea. Conversely, mathematicians were motivated by way of a number of mathematical problems raised through monetary theories. The sequence is designed to compile these mathematicians who have been heavily drawn to getting new difficult stimuli from monetary theories with these economists who're looking for potent mathematical instruments for his or her researchers. participants of the editorial board of this sequence includes following trendy economists and mathematicians: dealing with Editors: S. Kusuoka (Univ. Tokyo), A. Yamazaki (Hitotsubashi Univ.) - Editors: R. Anderson (U.C.Berkeley), C. Castaing (Univ. Montpellier II), F. H. Clarke (Univ. Lyon I), E. Dierker (Univ. Vienna), D. Duffie (Stanford Univ.), L.C. Evans (U.C. Berkeley), T. Fujimoto (Fukuoka Univ.), J. -M. Grandmont (CREST-CNRS), N. Hirano (Yokohama nationwide Univ.), L. Hurwicz (Univ. of Minnesota), T. Ichiishi (Hitotsubashi Univ.), A. Ioffe (Israel Institute of Technology), S. Iwamoto (Kyushu Univ.), okay. Kamiya (Univ. Tokyo), ok. Kawamata (Keio Univ.), N. Kikuchi (Keio Univ.), T. Maruyama (Keio Univ.), H. Matano (Univ. Tokyo), ok. Nishimura (Kyoto Univ.), M. ok. Richter (Univ. Minnesota), Y. Takahashi (Kyoto Univ.), M. Valadier (Univ. Montpellier II), M. Yano (Keio Univ).

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**Additional resources for Advances in Mathematical Economics Volume 11**

**Example text**

Econ. 3, 1–44 (2001) 6. : Uniform scalar integrability and strong law of large numbers for Pettis integrable functions with values in a separable locally convex space. J. Theoret. Probab. 13(1), 93–134 (2000) 7. : Dunford–Pettis–types theorem and convergences in set-valued integration. J. Nonlinear Convex Anal. 1, 37–71 (1999) 8. : Convex analysis and measurable multifunctions. Lectures Notes in Math 580 (1977) 9. : Fatou’s Lemma for unbounded Gelfand integrable mappings. CERNSEM, Universit Paris 1 (2002) 10.

Castaing et al. , then lim inf d(y, Cn ∩ α B ∗ ) = lim inf d(y, Cn ). 2. , C) of a subset C of E ∗ is identically +∞ if and only if C is empty. Thus, the distance function of a nonempty set is finite at every point (or, equivalently, at one point). 7(i) shows that w∗ − ls Cn is nonempty as soon as lim inf d(0, Cn ) is finite. The converse implication is straightforward, so that the following equivalence holds w ∗ − ls Cn = ∅ ⇔ lim inf d(0, Cn ) < +∞. n→+∞ The next result provides a sufficient condition for the existence of integrable selections for the sequential weak∗ upper limit multifunction in a dual space.

15, AMS, Providence, USA (1977) 11. : Measurability and integrability of the weak upper limit of a sequence of multifunctions. J. Math. Anal. Appl. 153, 226–249 (1989) 12. s. Sém. Anal. Conv. Univ. 100 (1985) 44 C. Castaing et al. 13. : Integrals, conditional expectations, and martingales of multivalued functions. J. Multivariate Anal. 7, 149–182 (1977) 14. : Core and Equilibria of a Large Economy. Princeton University Press, Princeton (1974) 15. : Weak sequential convergence in L 1 (µ, X ) and an approximate version of Fatou’s lemma.

### Advances in Mathematical Economics Volume 11 by Takuji Arai (auth.), S. Kusuoka, A. Yamazaki (eds.)

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