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$\newcommand{\R}{\mathbb{R}}$Suppose $\Omega$ is a bounded, convex domain in $\R^{m}$. Fix $x_1, x_2\in\Omega$ and an invertible matrix $A\in\mathrm{GL}^{+}(m)$ with positive determinant. Let $U\...

I have the following question, which intuitively seems it should be true but I wasn't sure how to prove it rigorously. Let $\delta, \varepsilon > 0$. Let $\Psi_i(w_1, w_2, \mathbf{v})$ be a ...