It has a natural measure μ μ ∗ ∗ such that μ μ ∗ ∗ ( X 0 ) = 1 and the restriction of μ μ ∗ ∗ to X n is μ μ n . The even Fock space F + ( L 2 ( X , μ μ ) ) can then be identified with the space of symmetric functions in L 2 ( X ∗ ∗ , μ μ ∗ ∗ ) whereas the odd Fock space F − − ( L 2 ( X , μ μ ) ) can be identified with the space of anti-symmetric functions. The identification follows directly from the isometric mapping L 2 ( X , μ μ ) ⊗ ⊗ n → → L 2 ( X n , μ μ n ) ψ ψ 1 ( x ) ⊗ ⊗ ⋯ ⋯ ⊗ ⊗ ψ ψ n ( x ) ↦ ↦ ψ ψ 1 ( x 1 ) ⋯ ⋯ ψ ψ n ( x n ) .