  Complementary relationships exist regarding interference properties of
particles such as pattern visibility, predictability and distinguishability.
Additionally, relationships are known between information gain $G$ and
measurement disturbance $F$ for entangled spin pairs. The question of whether a
similar complementary relationship between entanglement and measurement occurs
is examined herein. For qubit systems, both measurement on a single system and
measurements on a bipartite system are considered in regards to the
entanglement. It is proven that $\overline{E}+D\le 1$ holds where
$\overline{E}$ is the average entanglement after a measurement is made and for
which $D$ is a measure of the measurement disturbance of a single measurement.
For measurements on a bipartite system shared by Alice and Bob ,it is shown
that $\overline{E}+G\le 1$ where $G$ is the maximum information gain regarding
Alice's result that can be obtained by Bob. These results are generalized for
arbitrary initial mixed states and as well to non-Hermitian operators. In the
case of maximally entangled initial states, it is found that $D\le E_{L}$ and
$G\le E_{L}$ where $E_{L}$ is the entanglement loss due to measurement by
Alice. We conclude that the amount of disturbance and information gain that one
can gain are strictly limited by entanglement.
