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<Text-field style="Heading 1" layout="Normal"><Font encoding="UTF-8">converg\303\252ncia uniforme,</Font></Text-field>
<Text-field style="Text" layout="Normal"><Font italic="true">n.</Font> <Font encoding="UTF-8">a propriedade que toda a fam\303\255lia de fun\303\247\303\265es ou s\303\251rie sobre um determinado conjunto</Font> <Hyperlink linktarget="Dictionary:Definition/converge" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">convergem</Font></Hyperlink> <Font encoding="UTF-8">para todo c\303\241culo do conjunto, ou seja, para cada</Font> <Font family="MaplePi">e</Font>&gt;0 <Font encoding="UTF-8">existe um \303\272nico</Font> <Font italic="true">N </Font>tal que para todos os pontos do conjunto,  
   <Font family="MaplePi" encoding="UTF-8">\302\275</Font><Font italic="true">f<Font subscript="true">m</Font></Font>(<Font italic="true">x</Font>) - <Font italic="true">f<Font subscript="true">n</Font></Font>(<Font italic="true">x</Font>)<Font family="MaplePi" encoding="UTF-8">\302\275</Font> <Font family="MaplePi">&lt;</Font> <Font family="MaplePi">e</Font> 
para todos <Font italic="true">m</Font>, <Font italic="true">n</Font> <Font family="MaplePi">&gt;</Font> <Font italic="true">N</Font>, <Font encoding="UTF-8">e da mesma forma para a converg\303\252ncia uniforme quando</Font> <Font italic="true">x</Font> tende a um valor de <Font italic="true">a</Font>.  <Font encoding="UTF-8">Esta \303\251 a converg\303\252ncia com o</Font> <Font italic="true">uniforme</Font> ou <Hyperlink linktarget="Dictionary:Definition/Chebyshevnorm" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">norma de Chebyshev</Font></Hyperlink>.  <Font encoding="UTF-8">Uma s\303\251rie de pot\303\252ncias converge uniformemente em qualquer disco de raio estritamente menor que seu raio de converg\303\252ncia. O limite uniforme de uma sequ\303\252ncia de fun\303\247\303\265es cont\303\255nuas \303\251 cont\303\255nua, ao contr\303\241rio do limite de</Font> <Hyperlink linktarget="Dictionary:Definition/pointwiseconvergent" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman" encoding="UTF-8">converg\303\252ncia pontual</Font></Hyperlink> <Font encoding="UTF-8">que n\303\243o pode ser. Este \303\251 frequentemente o caso para a</Font> <Hyperlink linktarget="Dictionary:Definition/Fourierseries" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman" encoding="UTF-8">s\303\251ries de Fourier</Font></Hyperlink>.  Veja <Hyperlink linktarget="Dictionary:Definition/Dirichletscondition" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman" encoding="UTF-8">condi\303\247\303\243o de Dirichlet's </Font></Hyperlink>, <Hyperlink linktarget="Dictionary:Definition/Ascolistheorem" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">teorema de Ascoli </Font></Hyperlink>.</Text-field>
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