We derive Onsager-Machlup functionals for countable product measures on weighted $\ell^p$ subspaces of the sequence space $\mathbb{R}^{\mathbb{N}}$. Each measure in the product is a shifted and scaled copy of a reference probability measure on $\mathbb{R}$ that admits a sufficiently regular Lebesgue density. We study the equicoercivity and $\Gamma$-convergence of sequences of Onsager-Machlup functionals associated to convergent sequences of measures within this class. We use these results to establish analogous results for probability measures on separable Banach or Hilbert spaces, including Gaussian, Cauchy, and Besov measures with summability parameter $1 \leq p \leq 2$. Together with Part I of this paper, this provides a basis for analysis of the convergence of maximum a posteriori estimators in Bayesian inverse problems and most likely paths in transition path theory.

翻译：我们从序列空间的加权 $\ ell ⁇ p$ 子空间 $\ mathb{R ⁇ mathb{N ⁇ $ $ 来计算可计算的产品计量的 Onsager- Machlup 功能。 产品中的每一项计量都是以$\ mathb{R}$ 上一个允许足够经常的 Lebesgue 密度的参考概率度量的转换和缩放副本。 我们研究了与本类中措施的组合序列相关的Onsager- Machlup 函数的均匀和 $\ gamma$- convergence 。 我们利用这些结果来为 separable Banach 或 Hilbert 空间的概率度量度设定类似的结果, 包括高斯、 考奇 和 比索夫 度的概率度度量, 其总和参数为 1\leq p\leq 2 。 与本文第一部分一起, 这为分析Bayesian 问题和过渡路径理论中最可能路径的最大测算提供了基础。