  Given a real Banach space $\mathcal{X}$ and probability space $(\Omega,
\Sigma, \mu)$ we characterize the countable additivity of Henstock-Dunford
integral for Henstock integrable function taking values in $X$ as those weakly
measurable function $ g: \Omega \to \mathcal{X} $ for which $\{y^*g~: y^* \in
B_\mathcal{X}^* \} $ is relatively weakly compact in some separable Orlicz
space $ \mathcal{L}^{\overline{\phi}}(\mu) .$ We find relatively weakly compact
in some Orlicz space with Henstock-Gel'fand integral.

Functional Analysis