This paper concerns the isometric theory of the Lebesgue-Bochner function space
L
p
(
μ
,
X
)
{L^p}(\mu ,\,X)
where
1
>
p
>
∞
1 > p > \infty
. Specifically, the question of whether a geometrical property lifts from X to
L
p
(
μ
,
X
)
{L^p}\,(\mu ,\,X)
is examined. Positive results are obtained for the properties local uniform rotundity, weak uniform rotundity, uniform rotundity in each direction, midpoint local uniform rotundity, and B-convexity. However, it is shown that the Radon-Riesz property does not lift from X to
L
p
(
μ
,
X
)
{L^p}\,(\mu ,\,X)
. Consequently, Lebesgue-Bochner function spaces with the Radon-Riesz property are examined more closely.