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Sierpinski gave an example of a nonmeasurable subset of $\mathbb{R}^2$ such that all sections are singletons areand hence null sets. So the answer is in general no.
Sierpinski gave an example of a nonmeasurable subset of $\mathbb{R}^2$ such that all sections are singletons are hence null sets. So the answer is in general no.
Sierpinski gave an example of a nonmeasurable subset of $\mathbb{R}^2$ such that all sections are singletons and hence null sets. So the answer is in general no.
Sierpinski gave an example of a nonmeasurable subset of $\mathbb{R}^2$ such that all sections are singletons are hence null sets. So the answer is in general no.
