Nazdikshavii muntazam

Nazdikshavii muntazam, holati khususii mafhumi nazdikshavist. Agar baroi dilkhoh  ε > 0 chu­nin N = N(ε) mavjud boshad, ki ba­roi on nobarobarii | f(kh) —f_n(kh) | < ε hangomi p > N va baroi hamai nuqtahoi x-i majmui dodashuda ijro shavad, paydarpaii funksiyahoi f_n (x) ( n = 1,  2, …) dar majmui do­dashuda ba funksiyai hududii f(kh) muntazam nazdik shavanda nombda meshavad. Macfkfy, paydarpaii funkciyahoi f _n (x) = kh^p dar porchai

ba funkciyai hududii f(kh) =  0 muntazam nazdikshavanda mebo­shad, zero baroi oar guna 0 < kh <  ǀ f(kh) f_n (x)< ( )ⁿ < e agar p >l_n( ) /ln  ² boshad, in funksiya

dar porchai [O, 1] muntazam nazdikshavanda nameboshad.

Paydarpaihoi muntazam nazdikshavanda khosiyathoi baso muhim do­rand: masalan, funksiyai hududii pay­darpaii muntazam nazdikshavanda hamchunin funksiyai befosila mebo­shad va gayra. Dar tahlili matematikii Nazdikshavii muntazam teoremai Veyershtrass mavqei muhim dorad. Har guna funksiyai dar parcha befosilaro chun hududi paydarpaii bisyoruzvahoi muntazam nazdikshavanda ifoda kardan mumkin ast.