I ran across this question in my analysis textbook. I just cannot prove this.
Suppose $\mu$ is a complex measure on $X$ such that $\mu(X)=1$ and $|\mu|(X)=1$. Show $\mu$ is a positive real measure.
I ran across this question in my analysis textbook. I just cannot prove this.
Suppose $\mu$ is a complex measure on $X$ such that $\mu(X)=1$ and $|\mu|(X)=1$. Show $\mu$ is a positive real measure.