Brownian Motion

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120sadvanced (8/10)conceptual

Brownian motion (B_{t})_{t \geq 0} has the property that \sum_{i} (B_{t_{i}} - B_{t_{i - 1}})^{2} \to t in L^{2} as the partition mesh of [0, t] goes to 0 . What is the consequence for ordinary Riemann calculus on Brownian paths?