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Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.

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Measure of set of vectors whose outer product are bounded

Let consider the canonical Euclidean space $E = \mathbb{R}^n$, endowed with the Lebesgue measure $\mu$. Define the map $v_k: E^k \rightarrow \mathbb{R}$ that sends a $k$-uple $x_1,\cdots, x_k$ of vec …