I want to show that if C is a Jordan measurable and a measure 0 set then $\int_C 1 =0$ (this is, its Jordan Measure is zero)
My approach is to show that $L(X_C,P)=0$ for all partition $P$, But I am not sure in how to proceed in this. Thanks a lot for your help.
My definition of measure 0 is that there exist rectangles $R_1,R_2,\ldots$ such that: $C \subset \bigcup R_i$ and the the sum of the volumes $\sum v(R_i) < \epsilon$.
Jordan measurable for me is a set tha is bounded and its boundary has measure zero.