Let k be a positive integer, b ≠ 0 be a finite complex number, let P be a polynomial with either deg P ≥ 3 or deg P = 2 and P having only one distinct zero, and let \documentclass[12pt]{minimal}
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\begin{document}$${\mathcal{F}}$$\end{document} be a family of functions meromorphic in a domain D, all of whose zeros have multiplicities at least k. If, each pair of functions f and g in \documentclass[12pt]{minimal}
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\begin{document}$${\mathcal{F}, P(f)f^{(k)}}$$\end{document} and P(g)g(k) share b in D, then \documentclass[12pt]{minimal}
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\begin{document}$${\mathcal{F}}$$\end{document} is normal in D.