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==The theorem==
Let <math>\Lambda</math> denote a lattice in <math>\Re^n</math> and <math>\Gamma</math> the corresponding reciprocal lattice. The theorem of Petersen and Middleton<ref>petmid62</ref> states that a function ''f(.)'' that is wavenumber-limited to a set <math>\Omega \subset \Re^n</math> can be exactly reconstructed from its measurements on <math>\Lambda</math> provided that the set <math>\Omega</math> does not overlap with any of its shifted versions <math>\Omega + x </math> where the shift ''x'' is any nonzero element of the reciprocal lattice <math>\Gamma</math>. In other words, ''f(.)'' can be exactly reconstructed from its measurements on <math>\Lambda</math> provided that <math>\Omega \cap \{x+y:y\in\Omega\} = \phi </math> for all <math>x \in \Gamma\setminus\{0\}</math>.
==Implications==
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