Hello, I have a non-homework problem I have been working on for a while. Let F be a set of positive decreasing 1-lipschitz functions of integral unity and G an isomorphic (to F)set of 1-lipschitz functions. F and G are defined on R and Y respectively where y=x-f(x) in Y and g in G is precisely: g(y) =min{x,f(x)} (x in R). Further, define: g(y) = 0 for all x <= -f(0) and f(x) is 0 outside a compact set and for x <0. The question? Show that g is also of integral unity, that is:(adsbygoogle = window.adsbygoogle || []).push({});

\int_[-f(0), \infty) g(y) dy = \int_[0, \infty) f(x)dx. Thank you for any input-I just realized that the 'standard' change of variable does not apply or at least is not what I need so I am stuck.

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

Dismiss Notice

Join Physics Forums Today!

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

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

# Isomorphism and integral unity

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads - Isomorphism integral unity | Date |
---|---|

I Integrate a function over a closed circle-like contour around an arbitrary point on a torus | Today at 12:51 PM |

Natural isomorphism from V to V | Apr 29, 2011 |

R^n x R^m isomorphic to R^{n+m} | Apr 8, 2011 |

Cauchy real and dedekind real are equivalent or isomorphic | May 17, 2010 |

Is it possible for a Banach Space to be isomorphic to its double dual | May 9, 2008 |

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