Motivated by recent developments in the metrical theory of continued fractions for real numbers concerning the growth of consecutive partial quotients, we consider its analogue over the field of formal Laurent series. Let $A_n(x)$ be the nth partial quotient of the continued fraction expansion of x in the field of formal Laurent series. We consider the sets of x such that $\mathrm{deg}{A}_{n+1}(x)+\cdots +\mathrm{deg}{A}_{n+k}(x)\ge \mathrm{\Phi }(n)$ holds for infinitely many n and for all n respectively, where $k\ge 1$ is an integer and $\mathrm{\Phi }(n)$ is a positive function defined on $\mathbb{N}$. We determine the size of these sets in terms of Haar measure and Hausdorff dimension.

中文翻译：

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正式Laurent系列的连续分数的度量性质

受实数连续分数度量理论中有关连续部分商增长的最新发展的推动，我们考虑了其在正式Laurent系列领域的相似性。让${\mathrm{一种}}_{ñ}（X）$是形式Laurent级数中x的连续分数展开式的第n个商。我们认为x的集合使得$\mathrm{度}{\mathrm{一种}}_{ñ+\mathrm{1个}}（X）+\cdots +\mathrm{度}{\mathrm{一种}}_{ñ+ķ}（X）\ge \mathrm{\Phi }（ñ）$分别容纳无限多个n和全部n，其中$ķ\ge \mathrm{1个}$ 是一个整数， $\mathrm{\Phi }（ñ）$ 是定义为的正函数 $\mathbb{ñ}$。我们根据Haar测度和Hausdorff维度确定这些集合的大小。