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Problem 1 (cf. IMT 1.1.8). Let h and w be positive reals, and let A =...

Problem 1 (cf. IMT 1.1.8). Let h and w be positive reals, and let A = (0, h) and B = (w, 0) be the specified points in R 2 . Let T be the solid triangle determined by the origin, A, and B. For this problem, you cannot use

1. Show that, for each Epsilon> 0, we can find elementary sets E and F with the properties that E ⊆ T ⊆ F and m^2 (F \ E) <Epsilon

2. Show that T is Jordan measurable in R^2 and the Jordan measure of T is hw/2.

Jordan measure is the measure of a solid that is not necessarily an elementary set, like in our case we have a solid triangle T, we need to find an elementary set E \subsetek T \subsetek F and m^2(F\E)< Epsilon.

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