We prove that every usco multimap \(\varPhi :X\rightarrow Y\) from a metrizable separable space X to a GO-space Y has an \(F_\sigma \)-measurable selection. On the other hand, for the split interval \({\ddot{\mathbb I}}\) and the projection \(P:{{\ddot{\mathbb I}}}^2\rightarrow \mathbb I^2\) of its square onto the unit square \(\mathbb I^2\), the usco multimap \({P^{-1}:\mathbb I^2\multimap {{\ddot{\mathbb I}}}^2}\) has a Borel (\(F_\sigma \)-measurable) selection if and only if the Continuum Hypothesis holds. This CH-example shows that know results on Borel selections of usco maps into fragmentable compact spaces cannot be extended to a wider class of compact spaces.

我们证明，从可量化的可分离空间X到GO空间Y的每个usco多图\（\ varPhi：X \ rightarrow Y \）都有一个\（F_ \ sigma \）可测量的选择。另一方面，对于分割间隔\（{\ ddot {\ mathbb I}} \）和投影\（P：{{\ ddot {\ mathbb I}}}} ^ 2 \ rightarrow \ mathbb I ^ 2 \ ）到单位平方\（\ mathbb I ^ 2 \）上的usco多图\（{P ^ {-1}：\ mathbb I ^ 2 \ multimap {{\ ddot {\ mathbb I}}} ^ 2} \）有一个Borel（\（F_ \ sigma \）（可衡量的）选择，且仅当连续体假说成立时。此CH示例显示，关于usco映射的Borel选择进入破碎的紧凑空间的已知结果无法扩展到更广泛的紧凑空间类别。