Let X be a set and $\mathcal{A}\subseteq \mathcal{P}(X)$ be a family closed under finite intersections such that $\varnothing ,X\in \mathcal{A}$. If $\psi =o,\omega ,\gamma$, then $\mathrm{\Psi }(\mathcal{A})$ is the family of those ψ-covers $\mathcal{U}$ for which $\mathcal{U}\subseteq \mathcal{A}$. In [3], properties $({\mathrm{\Psi }}_{\mathbf{\text{0}}})$ of a family $F\subseteq {}^X\mathbb{R}$ of real functions have been introduced. The main result of the paper Theorem 4.1 reads as follows: if $\mathrm{\Phi }=\mathrm{\Omega },\mathrm{\Gamma }$ and $\mathrm{\Psi }=\mathcal{O},\mathrm{\Omega },\mathrm{\Gamma }$, then for any pair $〈\mathrm{\Phi },\mathrm{\Psi }〉$ different from $〈\mathrm{\Omega },\mathcal{O}〉$, X has the covering property ${\mathsf{S}}_{\mathrm{1}}(\mathrm{\Phi }(\mathcal{A}),\mathrm{\Psi }(\mathcal{A}))$ if and only if the family of non-negative upper $\mathcal{A}$-semimeasurable real functions satisfies the selection principle ${\mathsf{S}}_{\mathrm{1}}({\mathrm{\Phi }}_{\mathbf{\text{0}}},{\mathrm{\Psi }}_{\mathbf{\text{0}}})$. Similarly for ${\mathsf{S}}_{\mathrm{fin}}$ and ${\mathsf{U}}_{\mathrm{fin}}$. Some related results are also presented.

设X是一个集合并且$\mathcal{一种}\subseteq \mathcal{磷}(X)$ 是一个在有限交点下封闭的家庭，使得 $\varnothing ,X\in \mathcal{一种}$. 如果$\psi =○,\omega ,\gamma$， 然后 $\mathrm{\Psi }(\mathcal{一种})$是那些ψ -covers的家族$\mathcal{你}$ 为此 $\mathcal{你}\subseteq \mathcal{一种}$. 在[3]中，属性$({\mathrm{\Psi }}_{\mathbf{\text{0}}})$ 一个家庭的 $F\subseteq {}^X\mathbb{电阻}$已经介绍了真正的功能。论文定理 4.1 的主要结果如下：如果$\mathrm{\Phi }=\mathrm{\Omega },\mathrm{\Gamma }$ 和 $\mathrm{\Psi }=\mathcal{哦},\mathrm{\Omega },\mathrm{\Gamma }$，那么对于任何对 $〈\mathrm{\Phi },\mathrm{\Psi }〉$ 不同于 $〈\mathrm{\Omega },\mathcal{哦}〉$, X具有覆盖性质${\mathsf{秒}}_{\mathrm{1}}(\mathrm{\Phi }(\mathcal{一种}),\mathrm{\Psi }(\mathcal{一种}))$ 当且仅当家庭的非负上 $\mathcal{一种}$- 半可测实函数满足选择原则 ${\mathsf{秒}}_{\mathrm{1}}({\mathrm{\Phi }}_{\mathbf{\text{0}}},{\mathrm{\Psi }}_{\mathbf{\text{0}}})$. 同样对于${\mathsf{秒}}_{\mathrm{鳍}}$ 和 ${\mathsf{你}}_{\mathrm{鳍}}$. 还介绍了一些相关结果。