We’ll discuss two applications of forcing to analysis. (1) For every partition of a set of reals into countable sets, there is a transversal of the same Lebesgue outer measure. (2) The existence of a continuum-sized family of entire functions which take fewer than continuum values at each complex number is undecidable in ZFC plus the negation of the continuum hypothesis. Both results are joint work with Saharon Shelah.

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