We formalize the construction of decentralized data markets by introducing the mathematical construction of tokenized data structures, a new form of incentivized data structure. These structures both specialize and extend past work on token curated registries and distributed data structures. They provide a unified model for reasoning about complex data structures assembled by multiple agents with differing incentives. We introduce a number of examples of tokenized data structures and introduce a simple mathematical framework for analyzing their properties. We demonstrate how tokenized data structures can be used to instantiate a decentralized, tokenized data market, and conclude by discussing how such decentralized markets could prove fruitful for the further development of machine learning and AI.