...[0,1], and f is in C[0,1], there is a sequence {g_n} in D that converges...0,1]. From above, we have for ε>0, there is N such that |f(x)-hm(x)|<&epsilon...
...positive set A must have ν(A) > 0, there is nothing can show ...... W.l.o.g, we assume &nu...;-e for each n. But then if A is the union of all A_n's, we have ν(...
...proposition: Given any set A and ε>0, there is an open set O such that A is ...0)+ε/4 F' 利用相同的證明得到 there is open set O' ,O'包含F...
...數理資優班學過 If x and y are any two real numbers, then there is some rational number r between x and y. 你的題目應該加上x,y為實數 2009...
Let M=inf{f(x):x in S} (M may be +∞) then there is sequence <x_n> in S such that f(x_n)->M, as n...
... E, F be subsets of X with E ⊆ F. There are two cases:If F = ∅, then E = ∅, μ(E) = μ(...
... f and g are uniformly continuous, there is a δ>0 such that if x, y in D and...(x ; r) ⊂ c(A). i.e. c(A) is open. Hence, A is closed...
