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

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

2008-03-08

arxiv.org/abs/0803.1244v2

Mathematics

Combinatorics

29 pages

Scientific paper

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.

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