This question is related to recently created tag and the way its usage is suggested in the tag-info (revision history). But I thought it might be good to ask here, since people who know functional analysis might be able to answer.
Google search for riesz representation theorem for lp spaces suggests that this is used too. But it is question for somebody more knowledgeable of this area how common it actually is.
@MichaelGreinecker If you happen to be around, what do you think of the above. It is common to call $L_p^* \cong L_q$ "Riesz representation theorem" (or Riesz representation theorem for Lp-spaces)?
Is there a field of mathematics that considers multiplying functions in a manner analogous to matrix multiplication? For instance,
Let $\mathbf{x}$ is an $n$-dimensional vector such that $x_i=\sin(2\pi \frac {i} {n}))$, for $i=1,\ldots, n$.
Let $\mathbf{A}$ be an $n\times n$ matrix where $A_{i,...
Show that Egoroff's theorem continues to hold if the convergence is pointwise a.e. and $f$ is finite a.e. Am I allowed to use Egoroff's theorem to prove that statement? The proof of Egoroff's theorem doesn't presuppose it.
Is there a field of mathematics that considers multiplying functions in a manner analogous to matrix multiplication? For instance,
Let $\mathbf{x}$ is an $n$-dimensional vector such that $x_i=\sin(2\pi \frac {i} {n}))$, for $i=1,\ldots, n$.
Let $\mathbf{A}$ be an $n\times n$ matrix where $A_{i,...
