54 635
Assignments Done
Successfully Done
In November 2017
Your physics homework can be a real challenge, and the due date can be really close — feel free to use our assistance and get the desired result.
Be sure that math assignments completed by our experts will be error-free and done according to your instructions specified in the submitted order form.
Our experts will gladly share their knowledge and help you with programming homework. Keep up with the world’s newest programming trends.

Real Analysis Answers


286Free Answers by our Experts:

Ask Your question

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Search & Filtering

Q. Show that the real line is a metric space.
Q. Is d(x, y) =√(│x-y│) a metric space?(solve it)
Consider the Cantor-Lebesgue function F : C → R, where C is the Cantor set.
a) Show that F is continuous and actually F can be extended to the whole R so that it is continuous (to do
this, note that if (a, b) is an interval from the complement of C, then F(a) = F(b)).
b) Using (a), show that if f : R → R is continuous function and A is a measurable subset of R, then f(A) may
not be measurable.
c) Show that the inverse image of a measurable set under a continuous function is not always measurable
(compare with Problem 2).
Hint: For (c), notice that F is increasing, thus the function F(x) +x is strictly increasing (and continuous).
Therefore, F(x) + x has a continuous inverse...
Fixing x, show that the Taylor series of e
tx− t
2 is given by X∞
nHn(x). (Explain
also why the series converges.)
Show that if A, B ⊆ R^d are closed sets, then A + B is measurable (in fact A + B is an Fσ set). Show, however that A + B may not be closed.
Evaluate ∫∫∫z2dx dydz
,where S is the solid region between the spheres ρ =1 and
ρ = 2, by using spherical coordinates.
1/2 is a limit of the interval] - 2.5,1.5[, true or false

Find the upper and lower integrals of the function f defined by
f(x)= (7/2)-2x, ∀ x∈[1,3]
Is f integrable over the interval [1,3]? Justify.
Let b = supS where S is a bounded subset of R.
(a) Given epsilon > 0, show that there exists an s in S with b - (epsilon) ≤ s ≤ b
true/false? prove..
Every function differentiable on [a, b] is bounded on [a, b]