Math 617
.
.
Nw the
,
Df
A
:
Ex
;
Day 17
13
point
obvif
.
m
)
M,
,
&
Existence
mare
D
-
o
:
an
is
o
if
fnik
-
ida
R
,
ht B
,
he the
.
&
the
be
,
S
fr g
B
Bo
E
,
Hey
st
(Xx
=
Bt
.
¥
¥
=
:
D
as
( En D)
,
peruse
B
)
the
easier in
my
be
Hien
x
2n <
=
he
auf
finite
o
,
he
Eixti
.
mantle
spaces
then there exist
.
nine
a
)
,
see
was the
ref
So
.
¥
Bo
,
Eixfi
Bo
abebn
in
when
TE
S
tht
near
F
Ex
=
4
Sit
feed
dainty pre
it to
Ahn
.
Kohnogam
mama
-
.
obviyf dgdmdr fnik
is
mins
.
nd OH no (0×0) =µd0 )my 101=0
,
by
the
age
n
,
,
4k
,
the
.
an
&
grated
measure
peruse
.
Sic Bo ad the s ; disjoint
Ge
.
,
St
min
My
Eit Mx Fitmy
thy ghts
,
Fe
,
mane
shn its
"
nxleilmylfi )
=
th
.
0=0
nd D=
Eixti
for
so
,
¥
it
ndsi )
stlg to shtht
,
oh
i
,
so
tnthe
goal
is
to
.
attn
qwkn
by
both sides
mtgwty
.
x
&
y
.
Nate fist
f
.
f
=
all At
,
the abne qwlm ,}
SYXEHX
{
.
'')
dmyti
te
V.
?¥X#HX÷lD
=
,
xekyt Y
.
dnylyl
Nw fist
,
if
.
FZPEIHXEH
X ,÷klX .ly )
wet
many
.
then
a
finite
&
EEMX
Whose
mesewe
.
obviously
.
to the
to be to
goy
Fi
with oh
Mxlftuy (F)
trick
,
.
redu
na
my
V
as
dispnt
a
Mxleilmyl
a
)
YEH
)
Bo
is
finite additv:B ,
'
F
additive
no
¥
mins
writes
na
finitely
Si
fnik
,
Nn the
,
m
IF )
=µd#u ,
F)
Ex
to
.
ebmtg pooht pre
fall
,
The god . to Shu tht
-
My )
on
Ft
Ex
obvinf
S
&
Huhn Kdmogan theorem
define
Mo 151
which
,
this
when lei ) <
"
cdledm
(
sine
*
nxxny ) I
wt to
we
.
Now
to
)
Mx
Y
Ei
Ut IKMYMD & H, My
:
Measure
X= ¥Y
at
.
.
¥
R=
she
Th Bts
spare
pooht nestle
a
finite
a
fnik
(Xx
m
1
Prof
is
spae
Patt
f
Uniqueness
mlehenxxny
The
)
m
men
,
,
I
X
finite
g
.
Also IR L ,
them
(
spa
Mease
paht
He
to define
fxx
& ntgte writ
.
y
:
Sho
:
{
)
nylf
X ,±lx)
it
LHSB
The
,€X#HX,=k
)
went
RHS ,
Far the
.
by
He
dny
§
hm
Mmotme
Gruyere Than
time
't 'd
HXF
FIXE
§
Xeitdxeihldmy
¥
,
4¥
f
lmikaaditvitg
rt9H=k±
SYXEIHXFIH
If
by
,
dmy
4)
"
buy )
.
¥
=
)
Xeitdnylfi
.
,
So pithy this tgdhr
we
,
let
see
,
F)
Xeklnyl
Of
¥
=
.
Xeitxlnylfil
={,X,÷lDmyH
I
course , the
thy hppyuhn
sue
new
µ
,
we
dmxld
nxletuyltt
So
,
B
a
pre
shots the
-
muse
audits
&
in
we
intent
=
{
am
the
w
.
rt
.
x
:
XE 'd myth dnxlxl
=
.
.
=
.
.
apply
theorem
.
-
Kohogow
Li
to get
.
,
,
Huhn
If nxleilnylfi)
a
wife
mere
Mxxmy
ukih
extols µ
.
&
B.