Reference for a proof of which 2-increasing functions are joint cdf's Can somebody give me a reference giving the detailed statement and proof of the fact that the joint cdf's of positive Borel measures $\mu$ on $\mathbb{R}^2$, so 
$$F(a,b) = \mu(\{(x,y) : x \leq a, y \leq b\})$$ 
are the 2-increasing functions satisfying a short list of axioms.   I wanted to mention this in a real variables course I am teaching, as a generalization of the well known 1 variable case that is in all the usual books, but dont have the time now to re-derive it.
Added: OK, I rederived it, but still would like to know a reference in the literature...
 A: It seems relevant, at least for probability measures, to cite the literature on copulas and "Sklar's Theorem":

Sklar, A. (1959), "Fonctions de répartition à n dimensions et leurs marges", Publ. Inst. Statist. Univ. Paris 8: 229–231

Carlo Sempi's lengthy "An introduction to Copulas" begins with some interesting historical details of early interactions between Fréchet, Abe Sklar, and Bert Schweizer.  He notes that:

The proof of Sklar’s theorem was not given in (Sklar, 1959), but a
  sketch of it was provided in (Sklar, 1973). (see also (Schweizer &
  Sklar, 1974)), so that for a few years practitioners in the ﬁeld had
  to reconstruct it relying on the hand–written notes by Sklar himself;
  this was the case, for instance, of the present speaker.

Define $C$ to be a $d$-dimensional copula iff $C:[0,1]^d \to [0,1]$ is a joint cumulative distribution function with uniform marginal distributions. Then (see Sempi p.22-24 loc. cit.):
Thm. A function $C$ is a copula if and only if the following properties hold:
(1) When all the components of $u$ are $1$ except the j-th component $u_j$, then $C(u) = u_j$.
(2) $C$ is isotonic, i.e. when $u \le v$ in $[0,1]^d$ (componentwise comparison), $C(u) \le C(v)$.
(3) $C$ is $d$-increasing, i.e. for each hyperrectangle $B$, the $C$-volume of $B$ is nonnegative.
For the specific case $d=2$ we can restate that a bivariate copula is a function $C:[0,1]^2 \to [0,1]$ such that:
$$ \forall u \in [0,1], C(u,0) = C(0,u) = 0 $$
$$ \forall u \in [0,1], C(u,1) = C(1,u) = u $$
$$ \forall 0\le u\le u' \le 1, 0\le v\le v' \le 1,
 C(u',v') - C(u,v') - C(u',v) + C(u,v) \ge 0 $$
Of course this last condition is that $C$ is 2-increasing.
Sklar's theorem states that for any $d$-dimensional cumulative distribution function $F(x_1,\ldots,x_d)$, there exists a copula $C$ such that:
$$ F(x_1,\ldots,x_d) = C(F_1(x_1),\ldots,F_d(x_d)) $$
where $F_j(x_j) = F(x)$ with all but the j-th component of $x$ equal 1, and that given by $x_j$, i.e. the j-th marginal distribution of $F$.  Conversely, given a copula $C$ and marginal distributions $F_j$, $j=1,\ldots,d$, the above defines a $d$-dimensional cumulative distribution function.
The uniqueness of copula $C$ is only guaranteed on the product of the ranges of $F_j$'s, so $C$ will be unique if these marginal distributions are continuous, but in general we have only their right continuity.  Since the equation for $F$ in terms of $C$ and the $F_j$'s depends only on the application over the product of their ranges, one approach to fixing a unique copula is to use multilinear (bilinear) interpolation.
You might prefer to cite, as the Wikipedia page does for this material:

Nelsen, R. B. (2006). An Introduction to Copulas, Second Edition. New York, NY 10013, USA: Springer Science+Business Media Inc. ISBN 978-1-4419-2109-3.

