Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spaces of measurable functions   For a metrizable space $X$ and a finite measure space
$(\Omega,\mathfrak{M},\mu)$ let $M_{\mu}(X)$ and $M^f_{\mu}(X)$ be the spaces
of all equivalence classes (under the relation of equality almost everywhere
mod $\mu$) of $mathfrak{M}$-measurable functions from $\Omega$ to $X$ whose
images are separable and finite, respectively, equipped with the topology of
convergence in measure. The main aim of the paper is to prove the following
result: if $\mu$ is (nonzero and) nonatomic and $X$ has more than one point,
then the space $M_{\mu}(X)$ is a noncompact absolute retract and $M^f_{\mu}(A)$
is homotopy dense in $M_{\mu}(X)$ for each dense subset $A$ of $X$. In
particular, if $X$ is completely metrizable, then $M_{\mu}(X)$ is homeomorphic
to an infinite-dimensional Hilbert space.

17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph