We prove the existence of a competitive equilibrium in a production economy with infinitely many commodities and a measure space of agents whose preferences are price dependent. We employ a saturated measure space for the set of agents and apply recent results for an infinite dimensional separable Banach space such as Lyapunov's convexity theorem and an exact Fatou's lemma to obtain the result.

中文翻译：

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具有无限维商品空间和价格依赖偏好的大生产经济中的均衡

我们证明了在具有无限多种商品和偏好与价格相关的代理的度量空间的生产经济中存在竞争均衡。我们为一组代理使用饱和度量空间，并将最近的结果应用于无限维可分离 Banach 空间，例如 Lyapunov 的凸性定理和精确的 Fatou 引理，以获得结果。