= Solution
Choose a collection of <statistical paths> through $P_f$ that are <differentiable in quadratic mean>. A <statistical tangent set> at $P_f$ is the set of their <score functions>. In particular each member belongs to $L^2_0(P_f)$, by the <mean-zero score identity under quadratic-mean differentiability>.
A <statistical tangent set> records which first-order directions the chosen <statistical paths> can realize. Its closed linear span in <L2 space> is the <statistical tangent space>. \b[The tangent set consists of attainable scores; the tangent space also includes their <linear combinations> and $L^2(P_f)$ limits.]
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