# Possible applications

1. Nov 26, 2011

### Kreizhn

I was given a problem by a professor to prove the following problem:

Anyway, I have done this but am supposed to remark on possible applications. I'm not sure to what I could apply this though. Maybe something to do with ergodics? Any suggestions would be appreciated.

2. Nov 28, 2011

### Kreizhn

Any suggestions?

3. Nov 28, 2011

### HallsofIvy

Staff Emeritus
I take it you mean that $\Gamma$ is the set $\{(x, y)| y= f(x)\}$.

What do you mean by $\Gamma+ \Gamma$? How are you adding sets?

4. Nov 28, 2011

### Kreizhn

Yes, that is what I meant. Sorry for the sloppiness, though I believe it's not an uncommon shorthand.

Set addition is taken to be naive: nothing special like essential sums. So
$$A+B = \{ a+b: a \in A, b \in B\}$$

5. Nov 29, 2011

### Kreizhn

Anybody have any ideas?