Скачать или смотреть In Lebesgue integration, a Lebesguerectangle is one of the basic building blocksused

In Lebesgue integration, a Lebesguerectangle is one of the basic building blocksused to measure sets or approximateintegrals. A rectangle in this sense does notalways meań ashape you can draw on paper,but rather a product set formed from twOintervals on the real line. Forexample, youcan think of it as taking one interval alongthe x-axis and another along the y-axis, andthen combining them into arectangle-shaped region. These rectanglesare used to cover parts of the domain of afunction, and by summing their sizes, we can are used to cover parts of the domain of afunction, and by summing their sizes, we canstart to build an approximation of thefunction's íntegral. This is similar in spirit tohow Riemann integration uses subintervals,but the key difference is that Lębesguerectangles are more flexible and focus onsets of values rather than rigidiy dividing upthe axİs.

sin(z) da=2

The strength of Lebesgue rectangles lies intheir ability to adapt to the way a functionbehaves on sets of points. By assigning a can define areas and volumes even when theunderlying set is very irregular. For example,if a function is scattered across the domainin a way that would break traditional 642Riemann sums, Lebesgue- rectangles can stllhandle it. They allow us to focus on thevalues of the function and the measure ofthe sets where those values occur, ratherthan being restricted to fixed partitions. Thismakes them a key tool in extendingintegration to a much wider class offunctions.#math #maths #learning #mathematics #study #foryou #physics #coding #ai #chatgpt #education #stem #algebra #calculus #animation #manim #fyp #mathskills #school #college #highschool #university
#shorts #viral