Multifunctions of two variables: examples and counterexamples

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1. [1] J. Appell, E. De Pascale, H. T. Nguyêñ and P. P. Zabreĭko, Multi-valued superpositions, Dissertationes Mathematicae 345 (1995). Zbl0855.47037
2. [2] J. Appell, H. T. Nguyêñ and P. P. Zabreĭko, Multivalued superposition operators in ideal spaces of vector functions I, Indag. Math. 2 (4) (1991), 385-395; Zbl. 748.47050. Zbl0748.47050
3. [3] J. Appell, H. T. Nguyêñ and P. P. Zabreĭko, Multivalued superposition operators in ideal spaces of vector functions II, Indag. Math. 2 (4) (1991), 397-409; Zbl. 748.47051. Zbl0748.47051
4. [4] Z. Artstein and K. Prikry, Carathéodory selections and the Scorza-Dragoni property, J. Math. Anal. Appl. 127 (1987), 540-547; Zbl. 649.28011. Zbl0649.28011
5. [5] P. Brunovsky, Scorza-Dragoni's theorem for unbounded set-valued functions, Mat. Stručno-metod. Časopis 20 (1970), 205-213; Zbl. 215.216. Zbl0215.21601
6. [6] C. Castaing, Sur les équations différentielles multivoques, C. R. Acad. Sci. Paris 263 (1966), 63-66; Zbl. 143.311. Zbl0143.31102
7. [7] K. Deimling, Multivalued Differential Equations, de Gruyter, Berlin 1992. 
8. [8] V. V. Filippov, On Luzin's theorem and right-hand sides of differential inclusions (Russian), Mat. Zametki 37 (1985), 93-98 [= Math. Notes 37 (1985), 53-56]; Zbl. 588.34011. 
9. [9] V. V. Filippov, On Luzin's and Scorza-Dragoni's theorem (Russian), Vestnik Mosk. Univ. 42 (1987), 66-68 [= Mosc. Univ. Math. Bull., 42 (1987), 61-63]; Zbl. 617.28005. 
10. [10] A. Fryszkowski, Carathéodory type selectors of set-valued maps of two variables, Bull. Pol. Acad. Sci. Math. 25 (1977), 41-46; Zbl. 358.54002. Zbl0358.54002
11. [11] C. J. Himmelberg, Measurable relations, Fundamenta Math. 87 (1975), 53-72; Zbl. 296.28003. Zbl0296.28003
12. [12] C. J. Himmelberg and F. S. van Vleck, An extension of Brunovsky's Scorza-Dragoni type theorem for unbounded set-valued functions, Math. Slovaca 26 (1976), 47-52; Zbl. 32.28004. Zbl0328.28004
13. [13] J. Janus, A remark on Carathéodory-type selections, Matematiche 41 (1986), 3-13; Zbl. 678.28005. Zbl0678.28005
14. [14] T. Kaczynski, Unbounded multivalued Nemytskii operators in Sobolev spaces and their applications to discontinuous nonlinearity, Rocky Mountain J. Math. 22 (1992), 635-643; Zbl. 810.35172. Zbl0810.35172
15. [15] N. Kikuchi, On contingent equations satisfying the Carathéodory-type conditions, Publ. Res. Inst. Math., Kyoto Univ. 3,3 (1968), 361-371; Zbl. 197.131. Zbl0197.13106
16. [16] M. A. Krasnosel'skiĭ and A. V. Pokrovskiĭ, Systems with Hysteresis (Russian), Nauka, Moscow 1983 [Engl. transl.: Springer, Berlin 1988]; Zbl. 665.47038. 
17. [17] A. Kucia, On the existence of Carathéodory selectors, Bull. Pol. Acad. Sci. Math. 32 (1984), 233-241; Zbl. 562.28004. Zbl0562.28004
18. [18] A. Kucia, Extending Carathéodory functions, Bull. Pol. Acad. Sci. Math. 36 (1988), 593-601; Zbl. 771.28008. Zbl0771.28008
19. [19] A. Kucia, Scorza Dragoni type theorems, Fundamenta Math. 138 (1991), 197-203; Zbl. 744.28011. Zbl0744.28011
20. [20] A. Kucia and A. Nowak, On Carathéodory type selectors in a Hilbert space, Ann. Mat. Sil. 14 (1986), 47-52; Zbl. 593.54018. Zbl0593.54018
21. [21] A. Kucia and A. Nowak, On Filippov type theorems and measurability of inverses of random operators, Bull. Pol. Acad. Sci. Math. 38 (1990), 151-158; Zbl. 771.28009. Zbl0771.28009
22. [22] A. Kucia and A. Nowak, A note on Carathéodory type functions, Acta Univ. Carol. Math. Phys. 34, 2 (1993), 71-74; Zbl. 809.28007. Zbl0809.28007
23. [23] K. Kuratowski and C. Ryll-Nardzewski, A general theorem on selectors, Bull. Pol. Acad. Sci. Math. 13 (1965), 397-403; Zbl. 152.214. Zbl0152.21403
24. [24] V. L. Levin, Convex Analysis on Spaces of Measurable Functions and Applications in Mathematics and Economics (Russian), Nauka, Moscow 1985; Zbl. 617.46035. 
25. [25] S. Łojasiewicz, Some theorems of Scorza Dragoni type for multifunctions with applications to the problem of existence of solutions for multivalued differential equations, Math. Control Theory, Banach Center Publ. 14 (1985), 625-643; Zbl. 576.49024. 
26. [26] E.A. Michael, Continuous selections I, Ann. Math. 63,2 (1956), 361-381; Zbl. 71.159. Zbl0071.15902
27. [27] J. Myjak, A remark on Scorza-Dragoni theorem for differential inclusions, Čas. Pěstování Mat. 114 (1989), 294-298; Zbl. 701.34026. Zbl0701.34026
28. [28] V. V. Obukhovskiĭ, On periodic solutions of differential equations with multivalued right-hand side (Russian), Trudy Mat. Fak. Voronezh. Gos. Univ. 10 (1973), 74-82. 
29. [29] V. V. Obukhovskiĭ, Personal communication, 1989. 
30. [30] T. Rzeżuchowski, Scorza-Dragoni type theorem for upper semicontinuous multi-valued functions, Bull. Pol. Acad. Sci. Math. 28 (1980), 61-66; Zbl. 459.28007. Zbl0459.28007
31. [31] A. Spakowski, On superpositionally measurable multifunctions, Acta Univ. Carolinae 30 (1989), 149-151; Zbl. 705.28003. Zbl0705.28003
32. [32] W. Zygmunt, On the Scorza-Dragoni's type property of the real function semicon-tinuous to the second variable, Rend. Accad. Naz. Sci. XL 11 (1987), 53-63; Zbl. 654.28006. Zbl0654.28006
33. [33] W. Zygmunt, The Scorza-Dragoni's type property and product measurability of a multifunction of two variables, Rend. Accad. Naz. Sci. XL 12 (1988), 109-115; Zbl. 677.28004. Zbl0677.28004
34. [34] W. Zygmunt, Product measurability and Scorza-Dragoni's property, Rend. Sem. Mat. Univ. Padova 79 (1988), 301-304; Zbl. 649.28012. Zbl0649.28012
35. [35] W. Zygmunt, On the approximation of semicontinuous Scorza-Dragonians by the multifunctions of Carathéodory type, Rend. Accad. Naz. Sci. XL 13 (1989), 23-30; Zbl. 692.28005. Zbl0692.28005
36. [36] W. Zygmunt, A note concerning the Scorza-Dragoni's type property of the compact multivalued multifunctions, Rend. Accad. Naz. Sci. XL 13 (1989), 31-33; Zbl. 697.28005. Zbl0697.28005
37. [37] W. Zygmunt, Remarks on superpositionally measurable multifunctions (Russian), Mat. Zametki 48 (1990), 70-72 [= Math. Notes, 48 (1990), 923-924]; Zbl. 728.28010. 
38. [38] W. Zygmunt, The Scorza-Dragoni property (Polish), Thesis, M. Curie Univ. Lublin 1990; Zbl. 734.28013. 
39. [39] W. Zygmunt, On superpositionally measurable semi-Carathéodory multifunctions, Comm. Math. Univ. Carol. 33, 1 (1992), 73-77; Zbl. 756.28008. Zbl0756.28008
40. [40] W. Zygmunt, Personal communication 1994. 
41. [41] W. Zygmunt, On superpositional measurability of semi-Carathéodory multifunctions, Comm. Math. Univ. Carol. 35, 4 (194), 741-744. Zbl0821.28008