By Guillaume Carlier (auth.), Shigeo Kusuoka, Toru Maruyama (eds.)

ISBN-10: 4431000038

ISBN-13: 9784431000037

ISBN-10: 4431539794

ISBN-13: 9784431539797

**Research Articles**: G. Carlier, Duality and life for a category of mass transportation difficulties and monetary functions; Charles Castaing and Ahmed Gamal Ibrahim: sensible evolution equations ruled via m-accretive operators; Leonid Hurwcz and Marcel ok. Richter, Implicit services and diffeomorphisms with out C; Leonid Hurwicz and Marcel okay. Richter, Optimization and Lagrange multipliers: Non-C1 Constraints and minimum constraint skills; Takao Fujimoto, Jose A. Silva and Antonio Villar, Nonlinear generalizations of theorems on inverse-positive matrices; Shigeo Kusuoka, Monte Carlo process for pricing of Bermuda sort derivatives.- **Historical Perspectives**: Isao Mutoh, Mathematical economics in Vienna among the wars.- topic index.

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**Example text**

Firstly, it is easy to see that R n is equal to the set of all measurable selections of the measurable multifunction rn (. )B E. , E x E defined by is measurable. ) B E such that V n (t) = X n (t ) + Yn(t) for all t E [0 ,1]. Moreover there is W n E U such that Yn = rnw n . So, we have that V n = X n + rnw n E A Un + R n for all n . As A( t ) is accretive for each t E [0, 1], it is easy to check that A is accretive in L~ ([O , 1]). 7). 2) the graph of A is strongl y-weakl y sequentially c1osed.

95, 344-374 (1983) ä Adv. Math . Econ. 5, 55-63 (2003) Advancesin MATHEMATICAL ECONOMICS ©Springer-Verlag 2003 Nonlinear generalizations of theorems on inverse-positive matrices* Takao Fujimoto", Jose A. jp) Department of Economic Analysis, University of Alicante, 03071 Alicante, Spain Department ofEconomic Analysis , University of Alicante and IVIE, 03071 Alicante, Spain Received: August 2, 2002 Revised: September 2, 2002 JEL classification: C67 Mathematics Subject Classification (2000): 15A48 Abstract.

A(t)g(t) = (IH + AA(t))-lg(t) is a Borel function on [0, 1] when g is continuous. Consequently t ---+ (IH + AA(t)) -lg(t) is measurable when g measurable, by applying Lusin's theorem to g and Scorza-Dragoni's theorem to f. So A(t) satisfies (H 3)(b) . As the directional derivative f: (x ;v) of ft at the point x in the direction v is equal to the support function 8*(v ,8ft(x)) of 8ft at the point v, using inequality If(t , x) - f(t, y)1 S ß(t )llx - yll yields 8*(v, 8 f t(x)) = f: (x ;v) = inf ft(x + 8i - ft(x) 8> 0 S ß(t)llvll, so that 8ft (x) = A(t)x c ß(t )B H forall (t ,x) E [0,1] x H .

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

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