On the Definitions of Giffen and Inferior Goods

We consider Giffen goods for the very general setting of an upper semi-continuous utility function. Two not equivalent definitions for this notions are discussed. Concerning this we show that there exists a (well-defined) non-decreasing demand function \({\mathbb{R}}_{++} \rightarrow \mathbb{R}\) that is nowhere strictly increasing. Also we reconsider the relation between Giffen and inferior goods.