Homogeneous function

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A homogeneous function of degree p satisfies

LaTeX: f(ax) = (a^p)f(x) for all LaTeX: a.

It is positively homogeneous if we restrict LaTeX: a > 0. When the degree is not specified (even by context), it is generally assumed to be 1. For example, LaTeX: x is homogeneous, LaTeX: xy + x^2 is homogeneous of degree 2, LaTeX: x + x^2 is not homogeneous, and LaTeX: xy/(x+y) is positively homogeneous on the positive elements of LaTeX: {\mathbb R}^2.


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