arXiv subjects

Isidore Fleischer

Publications and source records attributed to Isidore Fleischer.

2 recordsLinked to original sources

arXiv2003

Change of Variable for Multi-dimensional Integral

The change of variable theorem is proved under the sole hypothesis of differentiability of the transformation. Specifically, it is shown under this hypothesis that the transformed integral equals the given one over every measurable subset on which the transformation is injective; that countably many of these subsets cover the domain of invertibility; and that its complement -- the domain of non-invertibility -- is measurable and so may be broken off and handled separately.

math.CA↗

arXiv2002

L1 Compactness of Bounded BV Sets

Functions, uniformly bounded in $BV$ norm in some bounded open set $U$ in $R^n$, are compact in $L_1(U)$. This result is known when $U$ has Lipschitz boundary [EG Th. 4 p. 176], [G 1.19 Th. p. 17], [Z 5.34 Cor. p. 227]; the proof for general $U$ here, after identifying the operator theoretic definition of bounded $BV$ norm with that of the Tonelli variation, appeals to the standard compactness criterion in $L_1$ [DS 21 TH. p. 301] [Y, p. 275] (For completeness, these two auxiliary results are also presented).

math.FA↗