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HW3 2.1. Integrability with respect to intersection

HW3 2.1. Integrability with respect to intersection

av Clas Oscar Josef Stenström -
Antal svar: 2

I first assumed that that saying that a function is Riemann-integrable with respect to the intersection of two functions meant that it is integrable with respect to both, separately, but that's probably wrong.

Perhaps understanding this is part of the task, but if anyone could shed any light on how this notation should be interpreted, that would be appreciated. 

Som svar till Clas Oscar Josef Stenström

Re: HW3 2.1. Integrability with respect to intersection

av Sofia Tirabassi -

You are correct.

You have to show that it us integrable with respect both alphas.

If you see an answer of mine, this exercise is a slight spin of an exercise from Rudin. Basically you have that integrable with respect of one alpha is equivalent to right continuous, and integrable with respect the other us equivalent to left continuous

Som svar till Clas Oscar Josef Stenström

Re: HW3 2.1. Integrability with respect to intersection

av Sofia Tirabassi -

You are correct.

You have to show that it us integrable with respect both alphas.

If you see an answer of mine, this exercise is a slight spin of an exercise from Rudin. Basically you have that integrable with respect of one alpha is equivalent to right continuous, and integrable with respect the other us equivalent to left continuous