Survey of Measurable Selection Theorems: Russian Literature Supplement

1978 ◽  
Vol 16 (5) ◽  
pp. 728-732 ◽  
Author(s):  
A. D. Ioffe
Keyword(s):  
Russian Literature ◽  
Measurable Selection ◽  
Selection Theorems

1.—On Measurable Selections

1974 ◽  
Vol 72 (1) ◽  
pp. 1-7 ◽  
Author(s):  
A. P. Robertson
Keyword(s):  
Measure Space ◽  
Hausdorff Space ◽  
Polish Space ◽  
Measurable Selection ◽  
Selection Theorem ◽  
Polish Spaces ◽  
Measurable Multifunction ◽  
Selection Theorems ◽  
Suitable Measure ◽  
Separable Metric Space

SynopsisMeasurable selection theorems are proved, for a compact-valued measurable multifunction into a Hausdorff space that is the continuous image of a separable metric space, and for a closed-valued measurable multifunction from a suitable measure space to a regular Souslin space. The connection between Polish spaces and certain subsets of the real line is related to a measurable selection theorem for multifunctions into a Polish space.

scholarly journals Nonlinear random operator equations and inequalities in Banach spaces

1992 ◽  
Vol 15 (1) ◽  
pp. 111-118 ◽  
Author(s):  
Antonios Karamolegos ◽  
Dimitrios Kravvaritis
Keyword(s):  
Banach Spaces ◽  
Existence Theorems ◽  
Random Operator ◽  
Measurable Selection ◽  
Hammerstein Integral Equation ◽  
Operator Equations ◽  
Deterministic Theory ◽  
Measurable Multifunctions ◽  
Selection Theorems ◽  
Monotone Type

In this paper we give some new existence theorems for nonlinear random equations and inequalities involving operators of monotone type in Banach spaces. A random Hammerstein integral equation is also studied. In order to obtain random solutions we use some results from the existing deterministic theory as well as from the theory of measurable multifunctions and, in particular, the measurable selection theorems of Kuratowski/Ryll-Nardzewski and of Saint-Beuve.

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