# Lebesgue integral(jordan measurable)

1. Nov 30, 2011

### gotjrgkr

Hi!

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 $\int$$_{A}$f = $\int$$_{I}$g where I is a large rectangle containg the set A and g is a function with domain I whose a value at x$\in$A is f(x) and a value at x$\in$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 $\int$$_{A}$f are equal.

Is my guess true??