= Hadamard differentiability
{c}
{title2=$\dot\Phi_s(a)$}
= Hadamard differentiable
{c}
{synonym}
A map on a subset of a <normed vector space> is <Hadamard differentiable> at $s$ if its directional difference quotients converge to a <continuous linear map> uniformly along all convergent sequences of directions: $t_j\to0$, $a_j\to a$, and $s+t_ja_j$ in the domain imply $(\Phi(s+t_ja_j)-\Phi(s))/t_j\to\dot\Phi_s(a)$. Tangential differentiability restricts the limit directions to a specified subspace. This is the regularity used by the <functional delta method>.
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