Recent content by mesarmath

thanks so we were looking for a volume, curve was the thing that makes me confused thanks again :)

hi, i have been studying for GRE subject and i saw this question but i could not solve it x , y and z are selected independently and at random from the interval [0,1], then the probability that x is bigger than y*z is ? the answer is 3/4 but i want to know how? , i guess it should...

thanks so much but your last implication was not so obvious, at least for me :) but i did it myself thanks a lot again

hi, i was reading about finitely generated ideals and there was a remark that ideal which consists of polynomials with no constant term, in the polynomial ring Z[x_1,x_2,x_3,,,,,,] , is not finitely generated. and i can not show it is not finitely generated any idea?

hi, i want to show that If R is a PID then a submodule of a cyclic R-module is also cyclic. do i need to use fundamental theorem for finitely generated R-module over R PID ? thanks in advance

the set of continuous functions is dense in the set of Lebesgue integrable functions So when we do the problem for a continuous function (i.e. riemann integrable) we can extend it to any lebesgue integrable function. am i wrong?

after 4 hours working :) i solved , here the steps 1-) change of u=nx and as n goes to infty [-n,n] goes to whole space 2-) after some operations and by dividing [-n,n] into 2n/p equal pieces with length p/n 3-) then again change of u=t+ip-p where -n^2/p < i < n^2/p, 4-) by riemann integration...

hi, i have a hard problem, i guess so, i am looking for any help g(x) is a bounded Lebesgue measurable function that is periodic i.e. g(x)=g(x+p). Then for every f \in L^1(\Re) lim_{n\rightarrow \infty}\int_{\Re}f(x)g(nx) dx=(\int_{\Re}f(x)dx)((1/p){\int_{0}^{p}g(x) dx) thanks for...