You haven't defined everything. What you have is certainly not true - your [tex] \left P_k \right[/tex] looks like an arbitrary sequence, and you have no restrictions on f.another simple question would it be true to say
[tex]\int_{a_{L}}^{b} f = lim_{k \rightarrow \infty }L(f,P_k)[/tex]
Again, be careful: this is Analysis, you can't afford to make intuitive decisions. ConsiderIntuitively, as your partition gets "finer and finer", the error of the lower (upper) sum gets less.
hello all
another simple question would it be true to say
[tex]\int_{a_{L}}^{b} f = lim_{k \rightarrow \infty }L(f,P_k)[/tex]
thanxs