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Statement: Let $ h(n,x): \mathbb{R} \times \mathbb{R^m} \rightarrow \mathbb{R}^m $ be a continuous function and $|h(n,x)| = o(|x|^2)$ near $x = 0,$ where $|h|$ and $|x|$ are the same norm in $ \mathbb{R^m}$.

Can somebody explain what does $|h(n,x)| = o(|x|^2)$ mean?

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    http://en.wikipedia.org/wiki/Big_O_notation#Little-o_notation2012-01-12

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I will put Dan's comment as an answer. Please see