Extension of local positive definite ${\mathbb{Z}}_2^n$-superfunctions

By defining a concept of boundedness for ${\mathbb{Z}}_2^n$-superfunction, we show that each local positive definite ${\mathbb{Z}}_2^n$-superfunctions, which is bounded in some sense, on a ${\mathbb{Z}}_2^n$-Lie supergroup has a positive definite extension to all of the ${\mathbb{Z}}_2^n$-Lie supergroup.