Problem 1323 (difficulty: 4/10)

Let \(\displaystyle A\subset\R^p\), \(\displaystyle B\subset\R^q\) be bounded sets. True or false?

(a) \(\displaystyle k^{(p+q)}(A\times B) = k^{(p)}(A)\cdot k^{(q)}(B)\).

(b) \(\displaystyle b^{(p+q)}(A\times B) = b^{(p)}(A)\cdot b^{(q)}(B)\).

(c) If \(\displaystyle A\) and \(\displaystyle B\) are measurable, then \(\displaystyle A\times B\) is also measurable and \(\displaystyle t^{(p+q)}(A\times B) = t^{(p)}(A)\cdot t^{(q)}(B)\).

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