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While reading economics papers, especially those related to economy with land, I often encounter the terms $L^\infty$ and the "weak* topology". They seem like very basic terms, but I couldn't find a b …

I often see papers in economic theory mentioning a duality between the price space and the commodity space. I think they refer to duality of vector spaces. I.e, the commodity space is a vector space, …

Consider an economy with a finite number of goods and a finite quantity of each good. Each agent $i$ has a preference-relation $\succeq_i$ which is a total, reflexive and transitive relation over the …

Given a state-space $X \subseteq \mathbb{R}^m$ and $n$ utility functions, $u_1,\ldots,u_n: X\to \mathbb{R}$, define a state $x\in X$ as Locally Pareto-efficient if it has an open neighborhood $N(x)$ s …

Let $f_1, f_2$ be two smooth strictly-quasiconcave functions. Do there always exist monotone transformations $g_1,g_2$ such that the sum $g_1\circ f_1 + g_2 \circ f_2$ is ​a strictly-​quasicon …

Consider an economy with some $n$ agents with continuous utility functions $u_1,\ldots,u_n$. It is easy to prove that a Pareto-optimal allocation exists: define the welfare of an allocation $x$ as: $W …

Consider a firm with zero marginal cost. If it gives the product for free, then all the demand is satisfied and the social welfare increases by the maximum possible amount; call this increase $W$. Bu …

Measure theory is widely used in the problem of fair division (aka "cake-cutting"). See the many papers about fairness in economics journals. For a particular example, see Tatsuro Ichiishi and Adam I …