For a finite set $X\subset \mathbb R^n$ the geometric median is defined as the point in $\mathbb R^n$ for which the sum of distances to all points of $X$ attains its minimum. Here is a wiki article:
https://en.wikipedia.org/wiki/Geometric_median
Question 1. Is there some standard contemporary mathematical book (or article or survey) that contains all the basic information on this topic? I was able to find the English translation of a classical article of Weizsfeld of 1937
http://link.springer.com/article/10.1007%2Fs10479-008-0352-z#/page-1
but I would like to learn of further sources.
Question 2. Clearly one can consider geometric medians of infinite sets, for example domains in $\mathbb R^n$ where one should minimize the integral of distance. What terminology is used in this case? Is this minimizing point still called the geometric median? Are there some nice sources?
Question 2a. I am interested in particular if there is some nice characterization of the geometric median (in the sense of Qustion 2) of a solid triangle in $\mathbb R^2$?