Let $\{x_k\}_{k\in\mathbb{N}}\subset\mathbb{R}^n$, $x\in\mathbb{R}^n$, such that: $x_k\to x$. Let $R>0$. Is true that: $\chi_{B_R(x_k)}\leq\chi_{B_{2R}(x)}$ a.e. on $\mathbb{R}^n$, for $k$ large? In this case can you give me a rigorous proof please?
2026-03-25 16:06:50.1774454810
Bound for a sequence of indicator functions
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