Mathematics · Advanced university
Uniform error of a function sequence · formula reference
A bound uniform in x proves more than pointwise convergence at a chosen x.
Formula
A bound uniform in x proves more than pointwise convergence at a chosen x.
||fₙ||∞ = sup |fₙ(x)|
Worked example
For f_n(x) = 25x/n on [0,1], calculate sup over x of |f_n(x)| when n = 72. Round the final result to 4 decimal places if needed.
The function is nonnegative and increasing in x; its maximum occurs at x = 1 and equals 25/72.
0.3472
Prerequisites and checking
Algebra; calculus or linear algebra as appropriate to the topic. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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