1 Y5 R; v" S' L, C( b% C課程內容; k1 n! U. ]5 N6 @- p3 Q7 o
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課程介紹與導論5 C1 n' w$ A5 J8 ] f& }
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Class2 6 f6 F8 ]$ i+ W5 ^. F7 j第一章 Measure theory5 v- F# s$ l' L5 R1 T- C6 P
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Class3 , j- \; I& O6 }/ n; j. s1 C- NSec.1.2. Measure * P. t( l) u9 \& d/ M
Sec.1.3. Outer Measure ' y. f0 x1 g8 L* m6 h% M8 p/ c. S! V$ p$ B* l. [
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Class4 . Y& o+ e1 ? l s/ ^Sec.1.4. Constructing outer measure: x* V2 L( D' L3 e" J" z$ j% U
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8 K c: m! m/ I3 V7 pClass5 * l" E( \$ r2 E. E1 aSec.1.5-1.6 Lebesgue measure W$ Q/ `! k8 o( W" _8 E, ?$ l4 x: T+ \& F7 w: }$ y+ K! z
6 \& x! t: o: n" h, t6 L# zClass6 3 `( j4 k1 t6 V0 TSec.1.7 Metric space ' I5 e" u" w! Z: z. \7 i , C8 p+ P3 ` m' t# |/ q , j5 [# |5 c0 @. p, uClass74 ^: {; y) ~% D. L1 V) a
Sec.1.8-1.9 Construction of metric outer measure0 ]7 r- P( ]. d# l) G9 I
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Class8 ) E+ k6 C/ {: rSec.1.9 Construction of metric outer measure % k6 M. B+ U0 z" e+ u' Q2 V# w6 B- ~% ~
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Class9; ~: e4 h) W1 k/ h
sec.1.10 Signed measure7 X$ s' ], H0 R4 t
+ Z! w1 _0 O6 l, {1 y
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Class10! s; i- n5 i, A" x) m
6 T# f4 d5 B, k' P4 { 2 z1 z' R: Z. d Q6 B+ h/ b% \/ F5 q5 PClass11 - q1 r" Z( V' v1 v: J第二章 Integration8 S" W+ c2 s" s9 k
Sec. 2.2 Operations on measurable functions . V& R$ U% V& _1 a# B h * Q' A& S+ y$ h: Z" i3 t3 f # g$ ^* k+ o" D! LClass12 ; c, E+ ]1 ^5 |% X6 k+ n9 _Sec 2.3. Egoroff’s Thm.# R6 R. C' R# h4 O- s
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Class13 : w8 I9 R6 `: y" }* k9 x* b7 ?' KSec 2.3 Egoroff’s Thm. $ _6 z+ v L7 p! a+ y/ g D, T; t3 c6 N: f& j& [! v
3 U* z2 ]7 T6 S6 N! v; R' x
Class140 U5 V0 |: y$ M: A8 a' {
Sec 2.4 Convergence in measure " E2 g+ j, u$ ?2 `9 _1 V2 N; W 3 ]* N/ K5 h Z; \) B 4 r4 g8 F: t0 ?2 a. GClass15 5 `6 Y" K: I* l; k0 Y" jSec 2.5 Integrals of simple functions ! c0 x& x, i1 D7 B) B ^ 7 ?. p" o' K9 @) R( u( B1 E ) b# L; h1 ~& o \. y+ Z v uClass16 8 J* _, g% j* {( p& T) q, r/ ~% ASec. 2.6 Integrable functions ; }7 F. X# s! Q0 N: E* @) Z* m. u4 k Y2 p2 K, Z0 t" `8 X2 |
& z; u6 E: B/ d% h! u1 Z7 XClass17 2 [; y0 r$ b8 a2 z ]# y$ n, o Q ! g" |; F5 N: r ?' ?0 u1 H; O" v) h6 R$ h* o# x
Class18 ; y% H, ?# \1 m' Z( B# f2 iSec. 2.7 Properties of integrals , C( \: \% u) |* }) y; a) O, C( u; ~ F* E
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Class19-20' ? S1 Q# i9 i7 i' }* L' T! c
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Class211 I% p& x4 P+ y% U
Sec.2.9 DCT 8 V" k. p0 Q6 ~ u8 q 2 L: h) G) T& I5 C& Y6 q, V: A; v( _' j- C9 [
Class22& v) {3 ]% ?$ u5 O
Sec. 2.10 Applications of DCT 2 e# m. y% a- ~& ~: Q+ e1 |9 `% F j: A; }& s! f* J. G: |
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Class23-24 & M3 w8 v6 T2 H; K0 X9 MSec 2.11 (Proper) Riemann integral' w: h& A! B8 {$ y3 B& J+ ~* ]
& c- p. S! @- T7 f5 A: a/ i$ u ' i* `: q8 W# f, \% s9 G9 eClass25' b2 l4 z' ?5 B) N( Y. \
2 _1 ?5 g% m8 l V' s3 r; W% |, g* I5 X& N; V
Class26# N4 t, p2 G$ P, R* i9 x- y& \
Sec. 2.13. Lebesgue decomposition 4 ]7 X! v% ?, ?& a6 S) Y $ N4 Q. j" _& O- g# m; A: X5 r: {4 B$ u& d2 [1 }# ?5 ?
Class272 B2 I0 Y& f4 p: s6 X
Sec. 2.13. Lebesgue decomposition ' j& L/ H# i9 V% u. o$ [% F( y% }2 W2 S, [0 ^6 Z M1 o
* ~' h9 G2 c& n' a. t" m# [Class28! L2 S9 A$ {3 Y. O, M+ N
Sec. 2.14 Fundamental Thm of Calculus on ( Z- S. M! O. O1 x* w2 Q% F 2 ?0 \; @2 S+ H; K8 V3 W( R- e3 o1 Y# R* H/ y* [, k% m) D5 R
Class292 G3 t0 r. L7 n& M* k6 |; p! ?/ b
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Class309 C$ h. w$ c2 z5 t3 G
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Class331 G4 v5 O8 K3 X2 `7 U
第三章 Metric spaces 6 A: ~2 z/ b8 E) v4 vSec. 3.1 Topological spaces & metric spaces- _/ G5 p1 J8 d
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Class34 ( [) ^ s' \8 t- d" s # y7 k& _2 y4 D$ @; c 8 `& h" j* Q" p3 \2 S$ MClass35 ' i) k- o [. G$ T- ?! U( w6 |8 l0 ~3 l, Q4 @
2 `# H6 [$ \+ @* f. mClass36 - f% S' v, I, Q- H% m+ A J, D0 }; c- E( H9 w$ n
7 h! g: d* J- C# d/ k5 Y+ RClass37 # y" I8 P# |9 V' w : g m& }, Q- _8 M' X( E ) H& J8 N) c8 Y: `, U9 BClass387 U" A; i2 J+ Z" f
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Sec.3.7 Stone-Weierstiass Thm. ; M$ O' C2 Z% _1 v4 a8 Y# `6 J; W2 u3 U. i5 L2 M
+ ~ s/ z; {8 v9 h( PClass42 & ?$ t5 Q9 A) ~1 q7 E. n) q+ V " \* i7 M0 I3 ~9 @, A% N8 G' E' y1 `+ u
Class43. n A; ]7 h u% V2 O
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Sec. 4.4 Linear Transformations . @* \1 A( u2 z+ x6 k7 e l4 n" r. j4 N7 Y( m) U" d7 w/ b$ f$ @# ]$ @- W. Q) j
Class472 {3 H K8 S, c. Q. O1 x
sec. 4.5 Principle of uniform bddness (Banach- Steinhaus Thm): t* `) [7 b3 B2 r
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