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We show that for any isotropic log-concave probability measure $\mu$ on$\mathbb R^n$, for every $\varepsilon > 0$, every $1 \leq k \leq \sqrt{n}$ andany $E \in G_{n,k}$ there exists $F \in G_{n,k}$ with $d(E,F) < \varepsilon$and $L_{\pi_F\mu} < C/\varepsilon$.

Neighborhoods on the Grasmannian of marginals with bounded isotropic constant