Let $X$ be a set, let $\mathbb{F}$ denote either $\mathbb{R}$ or $\mathbb{C}$, and let $(f_k)_{k=1}^{\infty}$ be a sequence of bounded functions $f_k:X\to\mathbb{F}$. Suppose that there exists a real number $M<\infty$ such that
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\begin{align*}
\|f_k\|_{\infty} \le M
\end{align*}