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TY - CHAP
TI - MULTIPLE AND ITERATED INTEGRALS
A2 - McLEOD, ROBERT M.
AB - Two complementary aspects of integration over multidimensional intervals are treated in this chapter. First, in Section 6.1, it is assumed that$\int_1 f $exists. Conclusions are asserted concerning the existence of iterated integrals and their equality to$\int_1 f $. This is Fubini’s theorem. The proof is postponed to Section S6.4. Section 6.2 attacks the complementary question of what can be said about existence of$\int_1 f $from the known properties of an iterated integral. Some necessary conditions are developed which permit the conclusion that$\int_1 f $does not exist. Other conditions are found which allow the conclusion that$\int_1 f $exists to flow from properties

EP - 176
ET - 1
PB - Mathematical Association of America
PY - 1980
SN - 9780883850459
SP - 149
T2 - The Generalized Riemann Integral
UR - http://www.jstor.org/stable/10.4169/j.ctt5hhb4z.11
VL - 20
Y2 - 2021/09/20/
ER -