PomeCorollary 19.2.8.9FB3E8CE18F7 Let $S,S'\in \mathcal{S}'(C)$. Assume that $\operatorname{vol}(S\cap S')>0$. Then we have
\[ d_{\mathrm{sg}}(S,S')=\operatorname{vol}(S)+\operatorname{vol}(S')-2\operatorname{vol}(S\cap S'). \]
Corollary 19.2.89FB3E8CE18F7
The same corollary appears in the main chapter and the appendix. The appendix proof is retained.
Proof. This is a direct consequence of 19.7.25 and (19.2.6). $\square$
Read the alternative statement and proof
Corollary 19.2.8.9FB3E8CE18F7 Let $S,S'\in \mathcal{S}'(C)$. Assume that $\operatorname{vol}(S\cap S')>0$. Then we have
\[ d_{\mathrm{sg}}(S,S')=\operatorname{vol}(S)+\operatorname{vol}(S')-2\operatorname{vol}(S\cap S'). \]
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