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12 p, 151.5 KB Local monotonicity of measures supported by graphs of convex functions / Cerny, Robert (Charles University (Praga, República Txeca). Department of Mathematical Analysis)
Let f ∈ C2 (R) satisfy f(0) = f 0 (0) = 0 and f 00(0) > 0. Then the 1-dimensional Hausdorff measure restricted to the graph of f is locally monotone near the origin in the sense that there exists σ > 0 such that the function r 7→ µf B(z,r) r is nondecreasing on (0, σ) for every centre z ∈ B(σ). [...]
2004 - 10.5565/PUBLMAT_48204_04
Publicacions matemàtiques, V. 48 N. 2 (2004) , p. 369-380  

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1 Cerny, R.
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