  Two measurements of $A$ and $B$ are carried out one after the other. The
measurements of $A$ are controlled by the parameter $\lambda_A$ in the Kraus
operator, where the measurements of $B$ are controlled by the parameter
$\lambda_B$. Strong measurements imply that the parameters in the Kraus
operators approach infinite large values while weak measurements are carried
out when the parameters approach zero. Here we prove that by repeating on the
two successive measurements of $A$ and $B$ then: (1) Average over all
measurements of $A$ is invariant of the measurement strength parameters
$\lambda_A$ and $\lambda_B$. It implies that all surprising results obtained in
weak measurements of $A$ are washed out when the average is taken. (2) If the
operators $\hat A$ and $\hat B$ commute then the mean value of $B$ as obtained
by taking the average of the results for $B$ over all measurements is invariant
of $\lambda_A$ and $\lambda_B$. Moreover it is exactly equal to the expectation
value of $\hat B$ as expected for strong measurements of $B$. (3) If $\hat A$
and $\hat B$ do not commute \textit{and} another condition given in this paper
is satisfied then the mean value of the results obtained for $B$ depends on the
value of $\lambda_A$ and not on the value of $\lambda_B$. An illustrative
possible experiment to show the effect of the strength of the measurements of A
on the results obtained for the measurements of B is given.
