Heat equation with general stochastic measure colored in time

A stochastic heat equation on $[0,T]\times \mathbb{R}$ driven by a general stochastic measure $d\mu (t)$ is investigated in this paper. For the integrator $\mu$, we assume the $\sigma$-additivity in probability only. The existence, uniqueness, and H"{o}lder regularity of the solution are proved.