, (ii)Let now {x, y} be an element of N ? (f, W ) We know that x, y ? F c = ?. Let [z , z ] ? [x, y] a connected component of F c ? [x, y]. If [z , z ] is, say, horizontal, since n F (·) [1] changes sign between z and z , so does ? 1 f , and by continuity there is w ? [z , z ] where ? 1 f (w) = 0. Calling z the closest point from w in x, y, z ?w ?, and by definition of N ? (F, W ), z is also at distance ? from ?F = {f = 0} The Geometry of Random fields, We indeed proved that |? 2 f (x)| 2? 1 It follows that |? 1 f (z)| Lip(? 1 f )?, |f (z)| Lip(f )?. References, 1981.
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