How to make sense of $A+B$ where $A$ and $B$ are sets. Suppose $A$ and $B$ are compact subsets of the complex plane $ \mathbb{C}$. How do I make sense of $A + B$ ?
My first thougt:
If one of the sets consist only of one point, say $A = \{ z: |z| \leq R \}$ and $B = \{ z_0 \}$ my guess would be that $A + B = \{ z: |z-z_0| \leq R_A \} $.
But how to make sense of $A+B$ when both sets consist of more than one points? I was unable to find any definition, so I hoped maybe someone here have seen this notation before.
Note: My problem is to evaluate an integral of the form
$$ \int_{ \partial ( A + B) } f(z) dz .$$
Thanks
 A: You can make sense of $A+B$ everytime when you do have an operation on your set.
When you are in $\mathbb{C}$ for example it will be
$$A+B=\{a+b : a \in A \wedge b\in B\}$$
So for example when you have 
$A=[0,1]$ and $B=[0,1]$ then you have $A+B=[0,2]$.
But there are more unexpected things like when $A=B$ are the Cantor set, then $A+B=[0,2]$.
A: The definition is 
$$
A+B=\{a+b : a\in A \text{ and } b\in B\}
$$
Regarding how to make sense of it:
Imagine that $A$ is a curve and $B$ is a region that you're going to use as a "brush". Thinking of $B$ as just a disk centered at the origin will suffice for starters. Drag the brush $B$ along the curve $A$, and the region you've painted is $A+B$. If $A$ is a "fat" set, rather than just a curve, you have to drag your brush $B$ over all points of $A$.
Look up "Minkowski sum". Like here, for example.
A: Usually $A + B$ is defined as $\{a + b \mid a \in A \land b \in B\}$. However it may also be used to refer to the disjoint union of two sets. Meaning that it can be $A + B := (A \times \{0\}) \cup (B \times \{1\})$ or some other trick to make sure they are disjoint. In particular this can be used to build the topological sum of two topological spaces if you define the obvious topology on $A + B$.
