diff --git a/src/measure/radon/c0.tex b/src/measure/radon/c0.tex index 22461a5..ff2114c 100644 --- a/src/measure/radon/c0.tex +++ b/src/measure/radon/c0.tex @@ -62,7 +62,7 @@ so \[ - \abs{\int \phi d\mu} \le \sum_{j = 1}^n |\mu(A_j)| + 2n\eps + \abs{\int \phi d\mu} \ge \sum_{j = 1}^n |\mu(A_j)| - 2n\eps \] As such a $\phi$ exists for all $\eps > 0$, $\norm{I_\mu}_{C_0(X; \complex)} \ge \sum_{j = 1}^n |\mu(A_j)|$. Since this holds for all such partitions, $\norm{I_\mu}_{C_0(X; \complex)} \ge |\mu|(X)$. Therefore the map $\mu \mapsto I_\mu$ is isometric.