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{| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>e</big> || <big>c</big> || <big>d</big> || <big>f</big> || <big>b</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> || <big>a</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>b</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>d</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>e</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>e</big> || <big>c</big> || <big>b</big> || <big>f</big> || <big>d</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> || <big>a</big> || <big>e</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>b</big> || <big>f</big> || <big>d</big> || <big>e</big> || <big>a</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>a</big> || <big>e</big> || <big>b</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>e</big> || <big>a</big> || <big>c</big> || <big>b</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>c</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>e</big> || <big>a</big> || <big>f</big> || <big>c</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>d</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>e</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>c</big> || <big>b</big> || <big>e</big> || <big>a</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>c</big> || <big>d</big> || <big>e</big> || <big>a</big> || <big>b</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>a</big> || <big>f</big> || <big>e</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>b</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>e</big> || <big>d</big> || <big>b</big> || <big>c</big> || <big>a</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>e</big> || <big>c</big> || <big>b</big> || <big>f</big> || <big>d</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> || <big>a</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>b</big> || <big>f</big> || <big>d</big> || <big>a</big> || <big>e</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>a</big> || <big>e</big> || <big>c</big> || <big>b</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>e</big> || <big>c</big> || <big>d</big> || <big>f</big> || <big>b</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> || <big>a</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>b</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>d</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>e</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>e</big> || <big>c</big> || <big>b</big> || <big>f</big> || <big>d</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> || <big>a</big> || <big>e</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>b</big> || <big>f</big> || <big>d</big> || <big>e</big> || <big>a</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>a</big> || <big>e</big> || <big>b</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>e</big> || <big>a</big> || <big>c</big> || <big>b</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>c</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>e</big> || <big>a</big> || <big>f</big> || <big>c</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>d</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>e</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>c</big> || <big>b</big> || <big>e</big> || <big>a</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>c</big> || <big>d</big> || <big>e</big> || <big>a</big> || <big>b</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>a</big> || <big>f</big> || <big>e</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>b</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>e</big> || <big>d</big> || <big>b</big> || <big>c</big> || <big>a</bigwikitex> |}
rollbackEdits.php mass rollback
<wikitex>{{TODO| bordert="1" cellpadding="4" align="center"НЕ ОЧЕНЬ ПОНИМАЮ, ЗАЧЕМ ВООБЩЕ ЭТО УТСВЕРЖДЕНИЕ ТУТ}}{{Теорема!style="background:#efefef;"| *!stylestatement="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>Если $f$ — функция ограниченной вариации ($f \in \bigvee(a</big>!style, b)$), то ее можно представить в виде разности монотонно неубывающих функций ($f ="background:#efefef;"| <big>b</big>f_1 - f_2$).!style="background:#efefef;"| <big>c</big>!styleproof="background:#efefef;"| <big>d</big>!styleВозьмем в качестве $f_1$ функцию $f_1(x) ="background:#efefef;"| <big>\bigvee\limits_a^x (f</big>)$, тогда по аддитивности она будет не убывать.|Определим как $f_2$ функцию $f_2(x) = f_1(x) -f(x)$. Докажем, что она монотонно не убывает.!style="background:#efefef;"| <big>e</big>| <big>e$a </big> || x_1 <big>ax_2 </big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>$. Надо доказать, что $f_1(x_1) - f</big> |(x_1) \le f_1(x_2) -!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>e</big> || <big>c</big> || <big>b</big> || <big>f</big> || <big>d</big> |(x_2)$, или что $f(x_2) -!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> || <big>a</big> |(x_1) \le f_1(x_2) -!stylef_1(x_1) ="background:#efefef;"| <big>c</big>\bigvee\limits_{x_1}^{x_2} (f)$ (используем утверждение 1).| <big>c</big> || <big>b</big> || <big>Но действительно $f</big> || <big>d</big> || <big>a</big> || <big>e</big> |(x_2) -!style="background:#efefef;"| <big>d</big>f(x_1) \le | <big>d</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> |(x_2) -!style="background:#efefef;"| <big>f</big>(x_1) | <big>\le \bigvee\limits_{x_1}^{x_2} (f</big> || <big>d</big> || <big>a</big> || <big>e</big> || <big>c</big> || <big>b</big> )$, ч. т. д. |}}
