The classical stochastic integral
∫
H
d
X
\int H dX
is defined for real-valued semimartingales
X
X
. For processes with values in a Banach space
E
E
, the stochastic integral
∫
H
d
X
\int H dX
is defined for locally summable processes
X
X
, using a measure-theoretical approach. We investigate the relationship between semimartingales and locally summable processes. A real-valued, locally summable process is a special semimartingale. We prove that in infinite-dimensional Banach spaces, a locally summable process is not necessarily a semimartingale.