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I have a guess. Could you give me your opinion about my guess??

Let A be a rectifiable set(or jordan measurable set).This is defined in a book "Analysis on manifolds" by munkres. You can refer to it in p.112-113.

Now, let f be a bounded function over the set A, and suppose f is integrable over A.

Then [itex]\int[/itex][itex]_{A}[/itex]f = [itex]\int[/itex][itex]_{I}[/itex]g where I is a large rectangle containg the set A and g is a function with domain I whose a value at x[itex]\in[/itex]A is f(x) and a value at x[itex]\in[/itex]I-A is 0.

Then under this assumption, A is measurable, f is also measurable on A, and f is lebesgue integrable over A and the lebesgue integral and [itex]\int[/itex][itex]_{A}[/itex]f are equal.

Is my guess true??

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# Lebesgue integral(jordan measurable)

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