Demand set

Define ${\displaystyle L}$ as the number of goods the agent might receive an allocation of. An allocation to the agent is an element of the space ${\displaystyle R+l}$; that is, the space of nonnegative real vectors of dimension ${\displaystyle L}$.
Define ${\displaystyle >p}$ as a weak preference relation over goods; that is, ${\displaystyle x>px'}$ states that the allocation vector ${\displaystyle x}$ is weakly preferred to ${\displaystyle x'}$.
Let ${\displaystyle e}$ be a vector representing the quantities of the agent's endowment of each possible good, and ${\displaystyle p}$ be a vector of prices for those goods. Let ${\displaystyle D(>p,p,e)}$ denote the demand set. Then: D(>p,p,e) = {x: px <= pe and x >p x' for all affordable bundles x'.