define F(x)=x, then uF is the lebesgue stiljes measure(adsbygoogle = window.adsbygoogle || []).push({});

duF=dx

Let y=x^2

we all know that how to transform [tex]\int f(y)dy [/tex] into [tex]\int f(x^2)2xdx [/tex] (***)

But how exactly would one use the transformation theorem ?

Ie. T be a measurable transformation from X to Y, u is a measure on X

[tex]\int_{Y}fduT^{-1}=\int_{X}fTdu[/tex]

I want to see the transformation theorem in action otherwise it's too abstract for me to understand. My question is, how would one use the transformation theorem to obtain the same result as equation (***)?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Transformation of lebesgue integral

Loading...

Similar Threads - Transformation lebesgue integral | Date |
---|---|

I Lebesgue Integral of Dirac Delta "function" | Nov 17, 2017 |

A Help with Discrete Sine Transform | Sep 29, 2017 |

I Fredholm integral equation with separable kernel | Jul 9, 2017 |

A Inverse Laplace transform of F(s)=exp(-as) as delta(t-a) | Feb 17, 2017 |

**Physics Forums - The Fusion of Science and Community**