Discuss whether or not the mapping (x mapsto|x|^{2}) (or its inverse image) is a homomorphism [ left(mathbb{R}^{d},

Question:

Discuss whether or not the mapping $x \mapsto\|x\|^{2}$ (or its inverse image) is a homomorphism

\[
\left(\mathbb{R}^{d}, \mathcal{B}\left(\mathbb{R}^{d}ight), N\left(0, I_{d}ight)ight) \xrightarrow{\|x\|^{2}}\left(\mathbb{R}, \mathcal{B}(\mathbb{R}), \chi_{d}^{2}ight)
\]

of probability spaces.

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