Mk Ex 3 11 6 Let D Be A Compact Set In R And F D R The Graph Of F Is The Subset G X Y Y F X C Rn 1 1 (27.98 KiB) Viewed 12 times
[Mk] stands for Analysis on Manifolds by J. Munkres.
: [Mk] (Ex. 3.11.6) Let D be a compact set in R”, and f → R. The graph of f is the subset G= {(x,y) y = f(x)} c Rn+1 (a) Show that Gf has Jordan content zero if f is continuous. (b) Show that Gf has Jordan content zero if D is a rectangle and f is integrable over D.
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→ R. The graph of f is the subset G= {(x,y) y = f(x)} c Rn+1 (a) Show that Gf has Jordan content zero if f is continuous. (b) Show that Gf has Jordan content zero if D is a rectangle and f is integrable over D.