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...我先證: f is continuous almost everywhere, then f is measurable Pf : Let E={x in [a,b], f is continuous at x}, F=[a,b]\E then [a,b]=E...

...rule please check the webpage http://www.ricciflow.com/moogle/mod/forum/discuss.php?d=12 let $$u=ap$$ and $$f=f(u)$$ at u=x then $$\frac{\partial f}{\partial p}(x...

...x1, ..., xn) in Rn, x >或= 0 means xi >或= 0 for all i. Let S ＝ {x in Rn: x >或= 0 and x1 +...+ xn ＝ 1}, a non-empty compact convex subset of ...

1)Since f_n -> f in measure, so for any f_(n_k) there exists f_(n_k(m)) -> f a.e.,hence (f...f a.e.,for this n_k, since n_k(m) is a subsquence of n_k and g_n -> g in measure, hence there is n_k(m_p) so that g_(n_k(m_p)) -> g a.e.hence f...

令 P(x,y)= -y, Q(x,y)= x 則 P(x,y), Q(x,y)在整個R^2皆為C^(1), 故在R上為C^(1). 根據Green s Theorem ∮(on C) P(x,y)dx + Q(x,y)dy =∫∫(on R) ( ∂ Q / ∂x - &part...

For any m,n with m>n in |N Let S_n(x)=Σ(1~n)u_k(x) =>|S...;(k=n+1~m)v_k(x)<ε for all x in E =>Σu_n(x) is nuiformly convergent...

...2) be a finite set in R^n. Select any two elements a, b in S and let δ=min{|x-a|, x in S and x≠a}>0, then Ball(a, δ/2...

變數變換(坐標變換): 令u=x^2-y^2, v=x^2+y^2=>x^2y^2=(v^2-u^2)/4 Jacobian J=∂(u,v)/∂(x,y)= 8|xy| = 8xy (x, y>=0) 原積分=∫49∫14 xy*8xy du dv =∫49∫14 2(v^2 - u^2) du dv =∫49 2(3v^2 - 21) dv = 1120 2008-11-01 23:18:10 補充： 謝謝! Jacobian之分子分母寫反了, J=1/(8xy...