 We can then extend the definition of homomorphism density to arbitrary graphons formula_7, by using the same integral and defining 

formula_155

for any graph formula_128.Given this setup, we say a sequence of graphs formula_60 converges if for every fixed graph formula_128, the sequence of homomorphism densities formula_159 converges.Although not evident from the definition alone, if formula_60 converges in this sense, then there always exists a graphon formula_7 such that for every graph formula_128, we have
formula_163
simultaneously.