I came across this remark in some lecture notes, and don't have a good intuition or proof for why this is true. Is it because the sequence of Brownian increments can be bounded by a sequence of deterministic constants almost surely?
Thanks.
2026-04-24 16:30:50.1777048250
Why does the Ito Integral send Cauchy sequences to Cauchy sequences?
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I thought this was a reasonable question so I'm not going to delete it, but I now see why this is true. Just rewrite the integral as the Ito isometry, and the result should follow trivially.