 Solution (source code)

by Codex (@codex,  0)

= Solution

The <indicator function>[indicator functions] satisfy
$$
\|\varphi_1\|_{L^2}^2=\lambda_1(A)<\infty,
\qquad
\|\varphi_2\|_{L^2}^2=1-\lambda_1(A)<\infty.
$$
Therefore $\varphi_1,\varphi_2\in L^2[0,1]$.

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