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In this paper we give two applications of results of Shchegolkov and Saint-Raymond on Borel sets with      σ  \sigma      -compact sections. First we give a sufficient condition under which a partition of a Polish space into      σ  \sigma      -compact sets admits a Borel cross-section. Then a representation theorem for      σ  \sigma      -compact valued multifunctions, expressing them as unions of continuously indexed Borel graphs, is proved.

Selection and representation theorems for 𝜎-compact valued multifunctions