# Selection theorem in L¹

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2006)

- Volume: 26, Issue: 1, page 123-127
- ISSN: 1509-9407

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topAndrzej Nowak, and Celina Rom. "Selection theorem in L¹." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 26.1 (2006): 123-127. <http://eudml.org/doc/271151>.

@article{AndrzejNowak2006,

abstract = {Let F be a multifunction from a metric space X into L¹, and B a subset of X. We give sufficient conditions for the existence of a measurable selector of F which is continuous at every point of B. Among other assumptions, we require the decomposability of F(x) for x ∈ B.},

author = {Andrzej Nowak, Celina Rom},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {multifunction; measurable selector; continuous selector; decomposable set},

language = {eng},

number = {1},

pages = {123-127},

title = {Selection theorem in L¹},

url = {http://eudml.org/doc/271151},

volume = {26},

year = {2006},

}

TY - JOUR

AU - Andrzej Nowak

AU - Celina Rom

TI - Selection theorem in L¹

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2006

VL - 26

IS - 1

SP - 123

EP - 127

AB - Let F be a multifunction from a metric space X into L¹, and B a subset of X. We give sufficient conditions for the existence of a measurable selector of F which is continuous at every point of B. Among other assumptions, we require the decomposability of F(x) for x ∈ B.

LA - eng

KW - multifunction; measurable selector; continuous selector; decomposable set

UR - http://eudml.org/doc/271151

ER -

## References

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- [8] A. Nowak and C. Rom, Decomposable hulls of multifunctions, Discuss. Math. Differ. Incl. Control Optim. 22 (2002), 233-241. Zbl1032.26025
- [9] Cz. Olech, Decomposability as a substitute for convexity, Multifunctions and Integrands: Stochastic Analysis, Approximation and Optimization, Proc. Conf. Catania, Italy, June 7-16, 1983 (G. Salinetti, ed.); Lecture Notes in Math., vol. 1091, Springer-Verlag, Berlin, 1984, pp. 193-205.
- [10] A.A. Tolstonogov and D.A. Tolstonogov, Lₚ-continuous extreme selectors of multifunctions with decomposable values: Existence theorems, Set-Valued Anal. 4 (1996), 173-203. Zbl0847.54019
- [11] D.H. Wagner, Survey of measurable selection theorems, SIAM J. Control Optim. 15 (5) (1977), 859-903. Zbl0407.28006

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