By Shigeo Kusuoka, Toru Maruyama
The sequence is designed to compile these mathematicians who're heavily drawn to getting new demanding stimuli from monetary theories with these economists who're looking powerful mathematical instruments for his or her learn. loads of monetary difficulties may be formulated as restricted optimizations and equilibration in their ideas. numerous mathematical theories were offering economists with quintessential machineries for those difficulties coming up in financial conception. Conversely, mathematicians were inspired by means of a number of mathematical problems raised by means of fiscal theories
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Additional info for Advances in mathematical economics. Vol.19
Gk /k is uniformly bounded on B D fy 2 jky xk Ä ıg. If ı > 0 is sufficiently small, then B is compact. gk /k has a convergent subsubsequence. gk /k does not converge to g uniformly on B. k/ /k . y/k < " y2B for some k, a contradiction. This completes the proof. Acknowledgements We are grateful to Toru Maruyama for his helpful comments and suggestions. We would also like to express gratitude to the anonymous referee for their helpful advice. A Theory for Estimating Consumer’s Preference from Demand 55 References 1.
Fuzzy Sets Syst 41(3):285–291 16. Jalby V (1992) Semi-continuité, convergence et approximation des applications vectorielles. loi des grands nombres. Technical report, Université Montpellier II, Laboratoire Analyse Convexe, 34095 Montpellier Cedex 05, France 17. Joo SY, Kim YK, Kwon JS (2006) Strong convergence for weighted sums of fuzzy random sets. Inf Sci 176(8):1086–1099 18. Kruse R (1982) The strong law of large numbers for fuzzy random variables. Inf Sci 28(3):233–241 19. Kwakernaak H (1978) Fuzzy random variables.
This completes the proof of our claim. x; v/ (resp. tI x; v/ (resp. tI x; v/) is proportional to v. x; v/ D 0. x; v/ > 0. x; v/ D 0 if and only if x is proportional to v. Step 3: choose any compact subset V of 2 . Fix any " > 0. x; v/k < kvk"g, where y1 ; y2 are as in Lemma 2. Because y1 ; y2 is continuous, W is open in V , and thus V 0 D V n W is compact. x; v/I x; v/k kvk Ä ": Ä 17 See Sect. 3. x; v/ 2 V 0 . x; v/ 2 W , a contradiction. Hence, x is not proportional to v. x; v/ is continuous on V 0 .
Advances in mathematical economics. Vol.19 by Shigeo Kusuoka, Toru Maruyama