cantor st :- consider [0,17, Divride fo,1] inte turee eIual Parts 8& middle remove the Open interval, /3 2/3 (3 , 23) - remove, 11 me Xt, div!de 3 Cqual both Co,/3] & {243,1] in parts and middie Open intervais remove the (22 = Eo, V3了UE多 /s7g]U[多] %3D tue union of Closed intervals each a 2 G is

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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can ton set ;- considen E0,13, Divide fo,1] into
turee e ual
Parts
remove the
middie
Open
intenval,
1/3
2/3
A = (3 , 2/2) remove,
Co,13] e るるi 3 C9ual
middle Open inter vais
me Xt, divde botn
pants
and
remonve
the
(2- Eo, V3了U[多ッ s 7gU [多]
union of
2 C1osed intervals each of
G is
tue
having
len gthb 3
tue m
レ
い
in
い
length
ソ3"
へ
union of 2" ciosed
137.
At
7 th
step,
is
tne
intervels:
each of
1engnt
Note:- Each
Cn is
a closed set.
Define, C =ņ Cn
cis calIed
cantor set.
cleariy, c is c1osed, Hence, cis measurablC
M (c) Ź M(Cn) =(2/3)"
for each nEN.
Hencen
McC) =
Transcribed Image Text:can ton set ;- considen E0,13, Divide fo,1] into turee e ual Parts remove the middie Open intenval, 1/3 2/3 A = (3 , 2/2) remove, Co,13] e るるi 3 C9ual middle Open inter vais me Xt, divde botn pants and remonve the (2- Eo, V3了U[多ッ s 7gU [多] union of 2 C1osed intervals each of G is tue having len gthb 3 tue m レ い in い length ソ3" へ union of 2" ciosed 137. At 7 th step, is tne intervels: each of 1engnt Note:- Each Cn is a closed set. Define, C =ņ Cn cis calIed cantor set. cleariy, c is c1osed, Hence, cis measurablC M (c) Ź M(Cn) =(2/3)" for each nEN. Hencen McC) =
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