ASHFORD UNIVERSITY LIBRARY
My Experience Using Ashford Resources
Christine White
GEN499: General Education Capstone (GSV1649E)
Instructor: TaNeisha Page
December 12, 2016
ASHFORD UNIVERSITY LIBRARY
We must understand that research is very important for on
MATH 6337: Homework 5 Solutions
4.14. Let f (x, y ) be as in Exercise 13. Show that, given > 0, there exists a closed set
F E with |E \ F | < such that f (x, y ) converges uniformly for x F to f (x) as y 0.
[Hint: Follow the proof of Egorovs theorem, usin
MATH 6337: Homework 4 Solutions
4.1. Prove the following
(i) Corollary 4.2: If f is measurable, then cfw_f > , cfw_f < +, cfw_f = +, cfw_a
f b, cfw_f = a, etc. are all measurable. Moreover, f is measurable if and only if
cfw_a < f < + is measurable for e
MATH 6337: Homework 3 Solutions
3.10. If E1 and E2 are measurable, show that |E1 E2 | + |E1 E2 | = |E1 | + |E2 |.
Solution. We may assume that both |E1 | , |E2 | < +, or else the result is trivially true.
Otherwise, since
(E1 E2 ) \ E2 = E1 \ (E1 E2 ),
E2
MATH 6337: Homework 2 Solutions
3.3. Construct a two-dimensional Cantor set in the unit square [0, 1] [0, 1] as follows:
subdivide the square into nine equal parts and keep on the four closed corner squares,
removing the remaining region (which forms a cr
MATH 6337: Homework 1
1.1. Prove the following facts, which were left as exercises.
(a) For a sequence of sets cfw_Ek , lim sup Ek consists of those points which belong to innitely
many Ek , and lim inf Ek consists of those points which belong to all Ek f
Math 6337 : Real Analysis I
Final Exam
14 December 2011
Instructions: Answer any 5 of the problems.
1. Prove that if 0 < < 1, there is no measurable subset E of R that satises
<
|E I |
<1
|I |
for every interval I in R.
Solution: We proceed by contradicti
Math 6337 : Real Analysis I
Mid-term Exam 2
04 November 2011
Instructions: Answer all of the problems.
1. Use Fubinis Theorem to prove that
A
lim
A
Solution: Write
0
1
=
x
sin x
dx =
x
2
ext dt,
0
and then consider the following integral,
A
0
sin x
dx =
x
Math 6337 : Real Analysis I
Mid-term Exam 1
23 September 2011
Instructions: Answer all of the problems.
1. Recall that the outer measure of E Rn is dened to be
vol(Ij ) : cfw_Ij is a cover of E by closed intervals in Rn
|E |e = inf
j
Dene a closely relat
Homework #6 (Math 6337, due 3/8 in class)
1. #16 in page 148 of text.
2. #19 in page 148 of text.
3. #22 (a) in page 149 of text.
4. #24 in page 150 of text.
5. Let fn (x) (n = 1P; ) be monotone increasing functions on [a; b] and
;2
1
suppose that the ser
MATH 6337: Homework 6 Solutions
5.1. If f is a simple measurable function (not necessarily positive) taking values aj on Ej ,
j = 1, 2, ., N , show that
N
f=
aj |Ej | .
E
j =1
[Hint: Use (5.24). ]
Solution. Using the hint, we have
N
f=
E
N
N
f=
Ej
j =1
aj
MATH 6337: Homework 7 Solutions
5.12. Give an example of a bounded, continuous function f on (0, ) such that lim f (x) =
x
0 but f Lp (0, ) for any p > 0.
/
Solution. An example is
f ( x) =
1,
1
,
ln(x)
xe
x e.
This function clearly satises the conditions
ANNOTATED BIBLIOGRAPHY
Annotated Bibliography on Minimum Wage
Christine White
GEN499: General Education Capstone (GSV1649E)
December 19, 2016
Instructor: TaNeisha Page
ANNOTATED BIBLIOGRAPHY
Introduction:
The global societal issue chosen for my final argu
Rich men
Christine White
SOC205: Social Theory (FAJ622DS)
Instructor: Sidra Montgomery
June 27th, 2016
Rich Men
Introduction
I found it very surprising and interesting that suicide is twice as common as homicide. We just
don't hear about it as much, becau
Reflecting on Global Citizenship and Personal Identity
Christine White
GEN499: General Education Capstone (GSV1649E)
Instructor: TaNeisha Page
December 5, 2016
Reflecting on Global Citizenship and Personal Identity
We base global citizenship as the way of
1
Does Bilingualism Improve Brain Functioning?
Christine White
PSY304: Lifespan Development (COE1546A)
Instructor: Courtney Plotts
December 7th, 2015
2
Does Bilingualism Improve Brain Functioning?
Introduction
Bilingualism is defined as having some abilit
RUNNING HEADER: Keyboard Entry of Running Headers
Keyboard Only Instructions for Inserting
Running Headers
Please note that these directions can be used with some types of screen reading technology.
The key commands are specific to Windows independent of
Circadian Rhythms
Christine White
ESE370: Learning & the Brain (CX1551A)
Instructor: Nancy Forbes
December 21, 2015
Circadian Rhythms
Circadian rhythms are mental, physical and behavioral changes people experience throughout
a 24 hour cycle, that has a re
1
Social Psychology Who, What, to Whom
Christine White
PSY301: Social Psychology (COF1429A)
Instructor: Debra Ozolnieks
July 5th, 2014
2
Social Psychology Who, What to Whom
Introduction
In this brief essay I will explain to you my understanding of what
Wh
My Life On Gender and Sexuality
Christine White
SOC307: Gender and Sexuality (FAK615DS)
Instructor: April Dreeke
April 18th, 2016
My Life On Gender and Sexuality
I was taught to do gender by my environment from a very young age. Growing up I learned
from
MATH 6337: Homework 10 Solutions
8.11. If fk f in Lp , 1 p < , gk g pointwise, and |gk | M for all k , prove that
fk gk f g in Lp .
Solution. By Minkowskis inequality,
|fk gk f g |p |fk gk f gk |p + |f gk f g |p M |fk f |p + |f gk f g |p .
Since gk g poin
MATH 6337: Homework 9 Solutions
8.1. For complex-valued, measurable f , f = f1 + if2 with f1 and f2 real-valued and measur
able, we have E f = E f1 + i E f2 . Prove that E f is nite if and only if E |f | is nite, and
2
2 1/2
f E |f |. [Hint: Note that E f
MATH 6337: Homework 8 Solutions
6.1.
(a) Let E be a measurable subset of R2 such that for almost every x R, cfw_y : (x, y ) E
has R-measure zero. Show that E has measure zero and that for almost every y R,
cfw_x : (x, y ) E has measure zero.
(b) Let f (
Homework #5 (Math 6337, due 2/27 in class)
1.
2.
3.
4.
5.
#4 in page 91 of text.
#7 in page 91 of text.
#17 in page 93 of text.
#19 in page 93 of text.
#24 in page 95 of text.
1