  We show that quantum measures and integrals appear naturally in any
$L_2$-Hilbert space $H$. We begin by defining a decoherence operator $D(A,B)$
and it's associated $q$-measure operator $\mu (A)=D(A,A)$ on $H$. We show that
these operators have certain positivity, additivity and continuity properties.
If $\rho$ is a state on $H$, then $D_\rho (A,B)=\rmtr\sqbrac{\rho D(A,B)}$ and
$\mu_\rho (A)=D_\rho (A,A)$ have the usual properties of a decoherence
functional and $q$-measure, respectively. The quantization of a random variable
$f$ is defined to be a certain self-adjoint operator $\fhat$ on $H$. Continuity
and additivity properties of the map $f\mapsto\fhat$ are discussed. It is shown
that if $f$ is nonnegative, then $\fhat$ is a positive operator. A quantum
integral is defined by $\int fd\mu_\rho =\rmtr (\rho\fhat\,)$. A tail-sum
formula is proved for the quantum integral. The paper closes with an example
that illustrates some of the theory.
