# Oka's lemma

In mathematics, **Oka's lemma**, proved by Kiyoshi Oka, states that in a domain of holomorphy in **C**^{n}, the function –log *d*(*z*) is plurisubharmonic, where *d* is the distance to the boundary. This property shows that the domain is pseudoconvex.

## References

- Oka, Kiyoshi (1953), "Sur les fonctions analytiques de plusieurs variables. IX. Domaines finis sans point critique intérieur",
*Jpn. J. Math.*,**23**: 97–155, doi:10.4099/jjm1924.23.0_97, MR 0071089

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