Recent content by dataphile

I know that the inequality will hold true for any L^p norm, but I am still having trouble finishing the proof for the particular case of the L^2 norm.

Homework Statement Let f: X \rightarrow \mathbb{R}^{n}. We say that \textbf{f} = (f_{1}, ..., f_{n}) is integrable if each component f_{k} is integrable, and define \int \textbf{f} d\mu = (\int f_{1} d\mu, ..., \int f_{n} d\mu). Show that if \textbf{f} is integrable, then | \int...