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When $X$ is unbounded we have to assume also that the leading form of $f$ is positive in $\\mathbb{R}^n\\setminus\\{0\\}$. We obtain strong convexity of $\\varPhi_N(x)=e^{e^{N|x|^2}}f(x)$ on possibly unbounded $X$, provided $N$ is sufficiently large, assuming only that $f$ is positive on $X$. 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