Let f,g: A R be integrable. (a) For any partition P of A and subrectangle S,...

  

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Let f,g: A R be integrable. (a) For any partition P of A and subrectangle S, show that Ms(f + g) < Ms(f) + M s(g) ms(f) + ms(g) < ms(f + g) and and therefore U(f + 9, P) SUG,P) + U(0,P). and L(f,P) + L(g,P) <Uf + g, P) (b) Show that f + g is integrable and SAs +g = Sas + Sa9. (c) For any constant e, show that Sacf = cSaf. %3D %3D Let f,g: A R be integrable. (a) For any partition P of A and subrectangle S, show that Ms(f + g) < Ms(f) + M s(g) ms(f) + ms(g) < ms(f + g) and and therefore U(f + 9, P) SUG,P) + U(0,P). and L(f,P) + L(g,P) <Uf + g, P) (b) Show that f + g is integrable and SAs +g = Sas + Sa9. (c) For any constant e, show that Sacf = cSaf. %3D %3D

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Solutong Given that bet A be a oc in R A R be intgg... View the full answer