A gyermek 6 (1912) 02

A gyermek A Magyar Gyermektanulmányi Társaság közlönye 6. évfolyam Budapest, 1912. A folyóirat 1908-ig a Gyermekvédelmi lap mellékleteként, 1909-től mint önálló lap jelent meg

Monge-Ampère measures for convex bodies and Bernstein-Markov type inequalities

We use geometric methods to calculate a formula for the complex Monge-Ampère measure, for a convex body and its Siciak-Zaharjuta extremal function. Bedford and Taylor had computed this for symmetric convex bodies. We apply this to show that two methods for deriving Bernstein-Markov type inequalities, i.e., pointwise estimates of gradients of polynomials, yield the same results for all convex bodies. A key role is played by the geometric result that the extremal inscribed ellipses appearing in approximation theory are the maximal area ellipses determining the complex Monge-Ampère solution Vk