Moments of Two-Variable Functions and the Uniqueness of Graph Limits

Understand

For a symmetric bounded measurable function W on [0,1]^2, "moments" of W can be defined as values t(F,W) indexed by simple graphs.

• We prove that every such function is determined by its moments up to a measure preserving transformation of the variables.
• This implies that the limit of a convergent dense graph sequence is unique up to measure preserving transformation.