Lebesgue measure and Fourier theory

[Jianphys17]

Hi everyone, in this days i was seeing a little of Fourier series and transform, and i wondered if it was necessary to better understand before the measure and Lebesgue integral before studying it. Or it's not necessary?

 

[micromass]

Hi everyone, in this days i was seeing a little of Fourier series and transform, and i wondered if it was necessary to better understand before the measure and Lebesgue integral before studying it. Or it's not necessary?

It's definitely not necessary. In fact, it is much better to do measure and Lebesgue integrals before Fourier theory. The only benefit of doing Fourier theory first is to see how difficult and incomplete the theory is with the Riemann integral and how more natural things become with the Lebesgue integral.