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Definitions. A subset Q of R is called an open rectangle if Q = (a, 6) x (c, d) for some -00 < a 0 there is a countable collection {Q:}, of open rectangles such that ACÜQ. and EIQil<. i=1 Show that A:= {(z,0) € R? :z€ R} C R? has 2-dimensional measure 0.

Definitions. A subset Q of R is called an open rectangle if Q = (a, 6) x (c, d) for some -00 < a 0 there is a countable collection {Q:}, of open rectangles such that ACÜQ. and EIQil<. i=1 Show that A:= {(z,0) € R? :z€ R} C R? has 2-dimensional measure 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Personal Hotspot :1 connection(s) 49% E Problem 5. Definitions. A subset Q of R? is called an open rectangle if Q = (a, b) × (c, d) for some -00 <a<b<oo and -00 <e<d<oo. The area of Q is defined to be Ja – b - |c – d and is denoted by QI. We say that A C R? has 2-dimensional measure 0 if for any e > 0 there is a countable collection {Qi}, of open rectangles such that and i=1 Show that A:= {(z,0) E R? : z E R} CR? has 2-dimensional measure 0.
Transcribed Image Text:Personal Hotspot :1 connection(s) 49% E Problem 5. Definitions. A subset Q of R? is called an open rectangle if Q = (a, b) × (c, d) for some -00 <a<b<oo and -00 <e<d<oo. The area of Q is defined to be Ja – b - |c – d and is denoted by QI. We say that A C R? has 2-dimensional measure 0 if for any e > 0 there is a countable collection {Qi}, of open rectangles such that and i=1 Show that A:= {(z,0) E R? : z E R} CR? has 2-dimensional measure 0.
5:19 וי 22ם al G".al 4:49 a) STEP-I A = (2,0) E R?: x ER] S RZ Le S(ai, bi)] be a seguence Covering R with bi-a; = 1 for any E> 0 Define Q; by we 2. (ai, b,) x -E/2 E/2 2i+1 A SU 2, Step2 b) STEP-2 19:1 2 €/2 E 19:1 = Ž 19:1 and =-> A has two dimen Sicned measure zero.
Transcribed Image Text:5:19 וי 22ם al G".al 4:49 a) STEP-I A = (2,0) E R?: x ER] S RZ Le S(ai, bi)] be a seguence Covering R with bi-a; = 1 for any E> 0 Define Q; by we 2. (ai, b,) x -E/2 E/2 2i+1 A SU 2, Step2 b) STEP-2 19:1 2 €/2 E 19:1 = Ž 19:1 and =-> A has two dimen Sicned measure zero.
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