Let $X_1,X_2,\cdots,X_n$ be random variables. Is it true that the $\sigma$-algebra generated by all sets of the form
$\{X_1\leq x_1, X_2\leq x_2,\cdots, X_n\leq x_n\} $ is the same as the $\sigma$-algebra generated by all sets of the form $ \{X_1 - X_2\leq x_1^\prime, X_2 - X_3 \leq x_2^\prime, \cdots, X_{n-1} - X_n \leq x_{n-1}^\prime, X_n \leq x_n^\prime \}?$
Thanks, Phanindra