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A demand set is a model of the most-preferred bundle of goods an agent can afford. The set is a function of the preference relation for this agent, the prices of goods, and the agent's endowment.
Assuming the agent cannot have a negative quantity of any good, the demand set can be characterized this way:
Define L {\displaystyle L} as the number of goods the agent might receive an allocation of. An allocation to the agent is an element of the space R + L {\displaystyle \mathbb {R} _{+}^{L}} ; that is, the space of nonnegative real vectors of dimension L {\displaystyle L}.
Define ⪰ p {\displaystyle \succeq _{p}} as a weak preference relation over goods; that is, x ⪰ p x ′ {\displaystyle x\succeq _{p}x'} states that the allocation vector x {\displaystyle x} is weakly preferred to x ′ {\displaystyle x'}.