International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2010 
International Tables for Crystallography (2010). Vol. B, ch. 1.3, p. 30

Let f be a complexvalued function over Ω such that exists for any given compact K in Ω; f is then called locally integrable.
The linear mapping from to defined bymay then be shown to be continuous over . It thus defines a distribution :As the continuity of only requires that , is actually a Radon measure.
It can be shown that two locally integrable functions f and g define the same distribution, i.e.if and only if they are equal almost everywhere. The classes of locally integrable functions modulo this equivalence form a vector space denoted ; each element of may therefore be identified with the distribution defined by any one of its representatives f.