I thought IV was assumed continuous based on your drawing. Still, I’d be surprised—and I would love to know about it—if you could find an function with a discontinuous integral and does not seem unfit to correctly model IV to me—both out of interest for the mathematical part and of curiosity about what functions we respectively think can correctly model IV.
I think that piecewise continuity and local boundedness are already enough to ensure continuity and almost-everywhere continuous differentiability of the integral. I personally don’t think that functions that don’t match these hypotheses are reasonable candidates for IV, but I would allow IV to take any sign. What are your thoughts on this ?
Thanks for your answer !
I thought IV was assumed continuous based on your drawing. Still, I’d be surprised—and I would love to know about it—if you could find an function with a discontinuous integral and does not seem unfit to correctly model IV to me—both out of interest for the mathematical part and of curiosity about what functions we respectively think can correctly model IV.
I think that piecewise continuity and local boundedness are already enough to ensure continuity and almost-everywhere continuous differentiability of the integral. I personally don’t think that functions that don’t match these hypotheses are reasonable candidates for IV, but I would allow IV to take any sign. What are your thoughts on this ?