Editing Central limit theorem (section)

====Density functions====
The [[probability density function|density]] of the sum of two or more independent variables is the [[convolution]] of their densities (if these densities exist).  Thus the central limit theorem can be interpreted as a statement about the properties of density functions under convolution: the convolution of a number of density functions tends to the normal density as the number of density functions increases without bound. These theorems require stronger hypotheses than the forms of the central limit theorem given above. Theorems of this type are often called local limit theorems. See Petrov<ref>{{Cite book|last=Petrov|first=V. V. |title=Sums of Independent Random Variables|year=1976|publisher=Springer-Verlag|location=New York-Heidelberg | isbn=9783642658099 | at=ch. 7|url=https://books.google.com/books?id=zSDqCAAAQBAJ}}</ref> for a particular local limit theorem for sums of [[independent and identically distributed random variables]].