AI 中文总结
本文在ℓ²中构造了一类任意余维（含无限余维）曲面上的显式曲面测度，建立了高斯-格林型公式与斯托克斯型恒等式，研究了ℱ-连续性与博雷尔可测性的关系，揭示了无限维空间的特有现象。
AI 中文摘要
本文在ℓ²中一类具有任意（可能无限）余维的曲面上给出了曲面测度的显式构造，这些测度由与固定高斯乘积测度相关的局部表示构造而成。随后建立了局部和整体的高斯-格林型公式，引入了最高次微分形式的概念，并推导了相关的斯托克斯型恒等式，还确定了由曲面定向诱导的边界定向。此外，本文研究了ℱ-连续性与博雷尔可测性之间的关系，揭示了无限维环境下特有的现象。
英文摘要
In this paper, we give an explicit construction of surface measures on a class of surfaces with arbitrary, possibly infinite, codimension in $\ell^2$. These measures are constructed from local representations associated with a fixed Gaussian product measure. We then establish local and global Gauss--Green-type formulas, introduce a notion of top-degree differential form, and derive an associated Stokes-type identity. We also determine the orientation of the boundary induced by the orientation of the surface. Moreover, therelationship between $\mathcal F$-continuity and Borel measurability is examined,which reveals a phenomenon specific to the infinite-dimensional setting.
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