Page 1

Displaying 1 – 7 of 7

Showing per page

Banach-valued Henstock-Kurzweil integrable functions are McShane integrable on a portion

Tuo-Yeong Lee (2005)

Mathematica Bohemica

It is shown that a Banach-valued Henstock-Kurzweil integrable function on an m -dimensional compact interval is McShane integrable on a portion of the interval. As a consequence, there exist a non-Perron integrable function f [ 0 , 1 ] 2 and a continuous function F [ 0 , 1 ] 2 such that ( ) 0 x ( ) 0 y f ( u , v ) d v d u = ( ) 0 y ( ) 0 x f ( u , v ) d u d v = F ( x , y ) for all ( x , y ) [ 0 , 1 ] 2 .

Bochner product integration

Štefan Schwabik (1994)

Mathematica Bohemica

A new definition of the product integral is given. The definition is based on a procedure which is analogous to the sum definition of the Bochner integral given by J. Kurzweil and E.J. McShane. The new definition is shown to be equivalent to the seemingly verey different one given by J.D. Dollard and C.N. Friedman in [1] and [2].

Currently displaying 1 – 7 of 7

Page 1