Specifically, it is impossible for a function f in L (R) and its Fourier transform ƒ̂ to both be supported on sets of finite Lebesgue measure. A more quantitative version is ‖ ‖ f ‖ ‖ L 2 ( R d ) ≤ ≤ C e C | S | | Σ Σ | ( ‖ ‖ f ‖ ‖ L 2 ( S c ) + ‖ ‖ f ^ ^ ‖ ‖ L 2 ( Σ Σ c ) ) .