A little question about the basics of Lebesgue integration. There is a theorem: if functions f and g are L-integrable then the function f+g is also L-integrable.(adsbygoogle = window.adsbygoogle || []).push({});

This may be dumb, but I wish to know about the reciprocal lemma. Let h be a L-integrable function and f and g be functions such that h(x) = f(x) + g(x). Are f and g L-integrable? I suppose it is truth because I cant see how, being f a not L-integrable function, h could yet be a L-integrable one. But I cant' see the proof. Does someone got a minute to help? Thanks.

**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!

# If h is L-integrable and f + g = h, then f and g also are

Loading...

Similar Threads for integrable | Date |
---|---|

A Getting a finite result from a non-converging integral | Thursday at 6:32 PM |

I Decomposing a Certain Exponential Integral | Apr 12, 2018 |

How to make this integral (which does not converge) be finite? | Apr 6, 2018 |

I "Imagine" a definite integral with a finite number of discontinuties | Mar 30, 2018 |

I Improper integrals | Mar 30, 2018 |

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