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I am looking for a reference to the following fact, which probably is known and could be proved somewhere by someone. Theorem. The linear hull of any linearly independent Borel set in a Polish ...

Let LSC = LSC([0,1]) be the set of non-negative, lower semi-continuous functions on the unit interval which take values in $\mathbb{R}_+ \cup \{\infty\}$. We use epigraph topology on LSC, i.e. a ...