MITICA) > £ tfxdx i
if ( finite 7 {ftxdxctn) and uff) cc L . R
.
anch that fpfflxidxc.to AM
side that µ> MAI
MAI = S f dx
fuit) is a rincasare , 6 - finite
Lost Rainy that I have to prove is
tifoso Itmeaus that if d- C- B LCA)
then µ (a) e-0 .
restate {flxidx-ffaxdxfcxlya.la ) Io
a conci
( up to A SET of menassimo)
viceversa il X-r xtr
pe is 6- finite and µ«2
Lutto tenerezza) .¥ is possibile to Constant f 20
.
Il = flxt.li, pelar. È
PÈRE Larix not immediate to see that
fine naasurahle and fi fcxldxc, and also
µ [FILA) e pela) .
and fi flxidx eta .HN .{ = { flxidx E ÉTÉ # µ .
[X X is a continuano R - variarle
g- µ, Borel meonioinducendoli
- o fan density (DISTRIBUTION)
L' Square X io a Normal r .v. of panna a µ ,6 .
H
of parametro a. b
don net aprly{ we don' t havea-dnnty.tldiscrete n .
v .
,
Xlw) Ex) .
Then If µ is Band 6-finite then µ con la written
in a
« L and CLL
µ=I matematica
if Atee × sua that f tg Lato has nreasvre zero .
2) If A is a naasvrahle set in irto
wL' (A) = { f : IR → IR neanche aiuterai § I a}
(if A =R} we go to the pariamo case)
3) LPCIRJ eff : Irish mai .
and web that
(PLA) = { f , meno .")
mezzanotte finche Heat
fdthi#| le c for ALMOST EVERY × .
Locatore : III#Iii J
Maior or l' (A)Ela
Ex
H ldx ⇐ +a
text -4 EUR) / I' ftdxeta .
Ex fede {lgxxeco.si) O elsewhea
flx)# PUR) ' ma .
but
1 head to put zona "¥ "
str on this spam of function m arder for example
to definire da motion of coniuge
Abstractdef.intX be a VEE on
IR (or on C)
Humana that ⇐X , yti xtyt X LEIR (ae a. XEX .
Assume that on X is
definendoNORM that is a function =
:X → Tetto)H . ll see- Hall
Hall = NORM of see
Hall e0 if end auff if se
2) if at IR XEX
Hill e la 1 Il xll ( ÈÌ ) -
3) llxtyll E dalla llyll- (triangolo inegualità)
In this case X is called e
NORMED Space
.
of Distante
this is agood alef . of distante
sintesi) d (Xix) -0 11011 -0
if dcx,g)⇒ ⇒ Xx-ylleo ⇒ xyeo ⇒ xeno
2) dlx ,g) =D (g.×)
dagli elly -xll Key) ll = Il (y -XIII Elly - xll
3) dcx,7) e dcx.yltdc.ge) V-K.ge EX
÷ ÷
Il
L: eo
A nonned space is COMPLETE (and in this case X ns called
BANACH SPACE) if
is complete µ , I.Di Intel
× ×» conduit.ie) - se * co
appropriate norme .
L'CIR) felici)
a) l' is a uectorial space tinca
7 , g e l' art ft
§ If tg lo" fÌ%ftg E L' CIR)
fa l'
IR <to
It reenains to check that
Alfio ⇒ fcx) O fanalino, a cuery ×
.
-
Adulteravano Analiticamente A. = { × Hflxlls, se} Ale { × I ¥ HAI ca} A- « si × 1 È IEI} A=È
Italia A-= È.am An E A
X.AI taxi an
7
> Infatuare= fa Lian) .
Lineo .
Affidano LI con define a motion of convergente
A
III. Ha-ftp.ho-linmflfnlxtffdldy
(CA) , III) is Complete Affi ! 17 ldx
LERI
f.gelata) lfc fara vey
II lgCx fara .co < × µ EHI tgcxl E ctk far abnast -tfxeiricau
Query × . IFCXIIEC V. XEIRIA Italo LCAURDEEO 19 IEK KXEIRIB LIDI -0
Il filo = inf { e > o su ch that
| If 1 E c aleuost curry whea)(it is aj.gg#anbechechedieany9 (fila = essential npreunun off =
= info [ Ip 17 , sack that{ - etere:⇒3
fu → f in la