Recent content by Jack3

Re: What is lim_(n→∞) ∫_(-∞)^∞〖〖 x〗^n e^(-n|x|) dm 〗? YEs。

Show that ∑_(n=1)^∞ cos^n (2^n x) converges for a.e. x, but diverges on a dense set of x’s . Show that \sum_{n=1}^\infty \cos^n (2^n x) converges for a.e. x, but diverges on a dense set of x’s .

Suppose {f_n} is a sequence of functions that converges almost everywhere to a function f and define F_n = sup_k=1,...n |f_n| . Show that if the integrals of F_n remain bounded as n goes to infinity, then lim_n ∫〖f_n dm〗 = ∫〖f dm〗.

What is lim_(n→∞) ∫_(-∞)^∞〖〖 x〗^n e^(-n|x|) dm 〗? What is lim_(n→∞) ∫_(-∞)^∞〖〖 x〗^n e^(-n|x|) dm 〗? Find the limit and prove your answer.

How should I compute the integral of the Cantor-Lebesgue function ∫_0^1〖F(x)〗 dm?

I am trying to use generators and relations here. Let M ≤ S_5 be the subgroup generated by two transpositions t_1= (12) and t_2= (34). Let N = {g ∈S_5| gMg^(-1) = M} be the normalizer of M in S_5. Describe N by generators and relations. Show that N is a semidirect product of two Abelian...

Let M be the space of all 2 × 2 complex matrices, satisfying 〖(X)bar〗^t = -X (skew-hermitian). Consider M as a vector space over R. Define a bilinear form B on M by B(X,Y) = -tr(XY) (1) Show that B takes real values, is symmetric and positive definite. (2) For any A ∈ M , define the...