## Question

###### Let Mm and N" be oriented manifolds. Endow M x N with the product orientation, that is, if TM MxN _ M and TN M xN 7 are the canonical projections on the elements of the product, adl and n respectively define orientations OH M and N_ then the orientation OH M x N is defined to be the orientation defined by TMW TNI: If a â‚¬ 0"(M) and 8 â‚¬ n"(N) have compact support, show thata x 8 := (Tira) ^ (TN8)has compact support and is a (m +n)-form o M x N. Then; prove Fubini $ theorem: a X

Let Mm and N" be oriented manifolds. Endow M x N with the product orientation, that is, if TM MxN _ M and TN M xN 7 are the canonical projections on the elements of the product, adl and n respectively define orientations OH M and N_ then the orientation OH M x N is defined to be the orientation defined by TMW TNI: If a â‚¬ 0"(M) and 8 â‚¬ n"(N) have compact support, show that a x 8 := (Tira) ^ (TN8) has compact support and is a (m +n)-form o M x N. Then; prove Fubini $ theorem: a X 8 = (J2) Ive)

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