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\begin{document}$$\mathcal{F}$$\end{document} be a complex foliation by Riemann surfaces defined by a trivial (in the differentiable sense) fibration π:M⟶B\documentclass[12pt]{minimal}
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\begin{document}$$\pi :M\longrightarrow B$$\end{document} but for which the complex structure on each fibre π-1(t)\documentclass[12pt]{minimal}
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\begin{document}$$\pi ^{-1}(t)$$\end{document} may depend on t. Let σ:B⟶M\documentclass[12pt]{minimal}
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\begin{document}$$\sigma :B\longrightarrow M$$\end{document} be a section of π\documentclass[12pt]{minimal}
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\begin{document}$$\pi $$\end{document} contained in a F\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal{F}$$\end{document}-relatively compact subset of M. We prove: for any F\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal{F}$$\end{document}-relatively compact open set U containing Σ=σ(B)\documentclass[12pt]{minimal}
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\begin{document}$$\Sigma =\sigma (B)$$\end{document} and any integer s≥0\documentclass[12pt]{minimal}
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\begin{document}$$s\ge 0$$\end{document}, there exists a function U⟶C\documentclass[12pt]{minimal}
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\begin{document}$$U\longrightarrow {\mathbb {C}}$$\end{document} of class Cs\documentclass[12pt]{minimal}
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\begin{document}$$C^s$$\end{document} nonconstant on any leaf of (U,F)\documentclass[12pt]{minimal}
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\begin{document}$$(U,\mathcal{F})$$\end{document}, meromorphic along the leaves and whose set of poles is exactly Σ\documentclass[12pt]{minimal}
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\begin{document}$$\Sigma $$\end{document}.
