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I am integrating something (specifically 2-forms, but I think this is a general statement) over a set B of (real) codimension 2 in a 4-manifold (CP_2). I've been told that the measure of a set of codimension 2 will vanish, but I don't really understand why. I've been thinking about exterior products and hodge duals but I can't seem to understand it from that direction. Does anyone have any insights?

Thanks!

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# Vanishing measure of a set with codimenon 2

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