scholarly journals Note on the theorem on change of variable in a Riemann integral

1981 ◽  
Vol 106 (1) ◽  
pp. 79-83
Author(s):  
Jiří Navrátil
Keyword(s):  
Riemann Integral ◽  
Change Of Variable

scholarly journals A Remark on the Change of Variable Theorem for the Riemann Integral

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1899
Author(s):  
Alexander Kuleshov
Keyword(s):  
Riemann Integral ◽  
Variable Formula ◽  
Entire Domain ◽  
Change Of Variable ◽  
Modern Form ◽  
Variable Theorem

In 1961, Kestelman first proved the change in the variable theorem for the Riemann integral in its modern form. In 1970, Preiss and Uher supplemented his result with the inverse statement. Later, in a number of papers (Sarkhel, Výborný, Puoso, Tandra, and Torchinsky), the alternative proofs of these theorems were given within the same formulations. In this note, we show that one of the restrictions (namely, the boundedness of the function f on its entire domain) can be omitted while the change of variable formula still holds.

scholarly journals Note on the theorem on change of variable in Riemann integral

1970 ◽  
Vol 095 (4) ◽  
pp. 345-347
Author(s):  
David Preiss ◽  
Jaromír Uher
Keyword(s):  
Riemann Integral ◽  
Change Of Variable

Improved correlation dimension estimates through change of variable

1992 ◽  
Vol 163 (4) ◽  
pp. 269-274 ◽  
Author(s):  
M. Lefranc ◽  
D. Hennequin ◽  
P. Glorieux
Keyword(s):  
Correlation Dimension ◽  
Change Of Variable

scholarly journals r-Dependence in Two-Point Orientation Coherence Functions

2000 ◽  
Vol 34 (4) ◽  
pp. 233-241
Author(s):  
Peter R. Morris
Keyword(s):  
Correlation Function ◽  
Weight Function ◽  
Bessel Functions ◽  
Unit Weight ◽  
Experimental Procedure ◽  
Change Of Variable

Functions are derived, which are orthonormal on the range r=0, 1, with weight function corresponding to the distribution of r in a typical experimental procedure for measurement of the two-point orientation–coherence (or orientation–correlation) function. These are obtained by making an appropriate change of variable in spherical Bessel functions, orthonormal on the range r=0, 1, with unit weight function. The effects of weight function and change of variable on the functions are considered.

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