EXAMPLE AND COUNTEREXAMPLES IN DOUBLE INTEGRAL AND ITERATED INTEGRAL

Kim, Byung-Moo; Kim, Byung-Moo

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P-ISSN3059-0604
E-ISSN3059-1309
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ISSN : 3059-0604

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Vol.2 No.2

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EXAMPLE AND COUNTEREXAMPLES IN DOUBLE INTEGRAL AND ITERATED INTEGRAL

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309

1995, v.2 no.2, pp.127-132

Kim, Byung-Moo (Chungju National Univ.)

Kim, Byung-Moo. (1995). EXAMPLE AND COUNTEREXAMPLES IN DOUBLE INTEGRAL AND ITERATED INTEGRAL, 2(2), 127-132.

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Abstract

[1] Show that ∫$\_$0/$\^$1/ [∫$\_$0/$\^$1/ f($\chi$,y)dy] d$\chi$ = ∫$\_$0/$\^$1/[∫$\_$0/$\^$1/ f($\chi$,y)d$\chi$] Counterexample: If pk denotes the k-th prime number, let S(pk) = (equation omitted), let S = ∪$\_$k=1/$\^$$\infty$/ S(pk), and let Q = [0, 1]${\times}$[0, 1]. Define f on Q as follows; f($\chi$, y) = 0 ($\chi$, y)$\in$S, f($\chi$, y) = 1 ($\chi$, y)$\in$Q - S.(omitted)

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Vol.2 No.2

EXAMPLE AND COUNTEREXAMPLES IN DOUBLE INTEGRAL AND ITERATED INTEGRAL

Abstract

한국수학교육학회지시리즈B:순수및응용수학