MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Hi!

I'm interested in some problems, but to be honest i'm not sure of the field they belong to.

Let $h(x,y)$ be a bivariate function on $X^2$, where $X$ is some nice topological space (for instance $[0,1]$, or $[0,1]^2$.)

  1. What is $$\inf_A \int_{A\times A} h(x,y)dxdy?$$ where $A$ belongs to the class of measurable sets (I think one can use other classes of sets, like the closed sets, or the open sets, etc...).

  2. What is $$\inf_Y \sum_{x,y\in Y} h(x,y)?$$ where $Y$ belongs to the class of finite sets. What is $$\inf_Y \sum_{x\neq y\in Y} h(x,y)?$$

I think the answers are difficult, but if one has any idea or an idea of a link with something else, it is already a lot.

share|cite|improve this question
    
Here is a possible connection: if you take the $Y$ in the discrete case to be subsets of some finite set then you have a clique problem in graph theory, where $h$ represents edge weights. – Niels Diepeveen Oct 6 '11 at 21:47
    
Yes it is interesting as well, could you tell me more or indicate a reference? – kaleidoscop Oct 7 '11 at 16:07

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.