Since Hart's  and Werner's  seminal papers, several conditions have been proposed to show the existence of equilibrium in an asset exchange economy with short-selling. In this note, we discuss the relationship between two no-arbitrage conditions. The first condition is the assumption that the individually rational utility set U is compact, as considered by Dana, Le Van and Magnien . The second is inconsequential arbitrage, introduced by Page, Wooders and Monteiro . The main result of this comparison is to show that the inconsequential arbitrage condition is stronger than the assumption that U is compact
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