How to define the median for bivariate function?

I know if we define a function f(x) and its cdf is F(x). The inverse function of cdf is inverseF.

I can define its median as follows: median = inverseF(0.5).

But if I want to get the median for a bivariate function f(x,y). How to define it? Thanks very much!

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You mean a distribution function $f(x)$ - right? Similar to Bob Jansen answer, the search for the notion of a quantile in higher dimensions is much more complicated than in dimension 1. –  Richard May 27 at 9:47

The standard median is not defined in multiple dimensions but a generalized notion exists as explained in this CrossValidated answer.

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thank you very much! –  eric May 25 at 2:41