Suppose X i and Y i are two sequences of Brownian motions with all of the Brownian motions independent of each other. Let   Prove that Z n converges weakly with respect to the topology of C([0, 1] 2 )...

Suppose Xⁱ
and Yⁱ
are two sequences of Brownian motions with all of the Brownian motions independent of each other. Let

Prove that Z_n
converges weakly with respect to the topology of C([0, 1]²) as n → ∞ to a Brownian sheet.