Lambda is the Lebesgue measure. Lambda with the asterisk on top and bottom are the outer and inner Lebesgue measures respectively. Problem 30. Prove that in general and (A) + λ* (B) < λ* (A U B)...
Please prove Problem 11 & 12 carefully
(note that m represents Lebesgue measure & m* represents
Lebesgue outer measure):
11. Let E c Rn be an arbitrary subset. Show that for all є > 0 there exists an open set G containing E with m(G) m"(E) +e. 12. Let E C Rn be a measurable subset. Show that for all € > 0 there exists an open set G containing Ewith m (G\ E) < є.
11. Let E c...
Problem 2 A brass tube of inner and outer diameters D,-2 cm and Do-3 cm, respectively, is used to transfer heat from ambient air flowing across the tube to cold refrigerant (R-22) flowing inside the tube. The ambient air is flowing at un-0.1 m/s, and To 30°C. The cold refrigerant flow rate is m 1 gs, and its mean temperature is Tm-20°C. (a) Find the overall heat transfer coefficient, UA (b) To enhance the heat transfer, 16 straight fins of...
Problem 3 (30): Steam at Too,1 340 °C flows in a cast iron pipe [k- 80 W/m.°C] whose inner and outer diameter are Di 6 cm and D2 -8 cm, respectively. The pipe is covered with a 4-cm thick glass wool insulation [k-0.05 W/ m°C]. Heat is lost to the surroundings at Too,2 - 21°C by natural convection and radiation, with a combined heat transfer coefficient of h- 18 W/m2 °C. Taking the heat transfer coefficient inside the pipe to...