R2 → R sei gegeben durch f ( x ) = ( 1 − | x | 2 ) χB1 ( 0 ) ( x ), wobei B1 ( 0 ) die Einheitskreisscheibe ist.
Finden Sie explizit eine monoton wachsende Folge (gm)m≥1 integrierbarer Treppenfunktionen gm :
R2 → R, die punktweise von unten gegen f konvergieren (in dem Sinne, dass für alle x ∈ R2 gilt limm→∞ gm(x) = f(x) und gm(x) ≤ gm+1(x) ≤ f(x) für m ≥ 1)!
www.mathematik.uni-mainz.deR2 → R be given by f ( x ) = ( 1 − | x | 2 ) χB1 ( 0 ) ( x ), where B1 ( 0 ) is the unit disc.
Find explicitely a monotone sequence (gm)m≥1 of integrable step functions gm :
R2 → R, which converge to f pointwise from below (i.e., for each x ∈ R2 it is limm→∞ gm(x) = f(x) and gm(x) ≤ gm+1(x) ≤ f(x) for m ≥ 1)!
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