This inner product space is conventionally denoted by ( L 2 , ⟨ ⋅ , ⋅ ⟩ 2 ) {\displaystyle \left(L_{2},\langle \cdot ,\cdot \rangle _{2}\right)} and many times abbreviated as L 2 {\displaystyle L_{2}} . Note that L 2 {\displaystyle L_{2}} denotes the set of square integrable functions, but no selection of metric, norm or inner product are specified by this notation. The set, together with the specific inner product ⟨ ⋅ , ⋅ ⟩ 2 {\displaystyle \langle \cdot ,\cdot \rangle _{2}} specify the inner product space.