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Which of the following statements is true? I. If is uniformly convergent on, then is convergent in the sense of. II. If is convergent in the sense of, then is pointwise convergent on. III. If is pointwise convergent on, then is convergent in the sense of.

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MCQs on Partial Differential Equations.


Which of the following statements is true?<br/> I. If<br><img src='https://www.fatskills.com/images2/GradExams/8B13178A-1194-4C15-9128-2366F6A0F9AB.png' height='20' width='37'/> is uniformly convergent on<br><img src='https://www.fatskills.com/images2/GradExams/E1E336DB-6F15-4579-89B8-FE039B799486.png' height='14' width='17'/>, then<br><img src='https://www.fatskills.com/images2/GradExams/8B13178A-1194-4C15-9128-2366F6A0F9AB.png' height='20' width='37'/> is convergent in the sense of<br><img src='https://www.fatskills.com/images2/GradExams/FA34593F-686D-487F-A186-47F5BA4EFED0.png' height='22' width='53'/>.<br/> II. If<br><img src='https://www.fatskills.com/images2/GradExams/8B13178A-1194-4C15-9128-2366F6A0F9AB.png' height='20' width='37'/> is convergent in the sense of<br><img src='https://www.fatskills.com/images2/GradExams/FA34593F-686D-487F-A186-47F5BA4EFED0.png' height='22' width='53'/>, then<br><img src='https://www.fatskills.com/images2/GradExams/8B13178A-1194-4C15-9128-2366F6A0F9AB.png' height='20' width='37'/> is pointwise convergent on<br><img src='https://www.fatskills.com/images2/GradExams/E1E336DB-6F15-4579-89B8-FE039B799486.png' height='14' width='17'/>.<br/> III. If<br><img src='https://www.fatskills.com/images2/GradExams/8B13178A-1194-4C15-9128-2366F6A0F9AB.png' height='20' width='37'/> is pointwise convergent on<br><img src='https://www.fatskills.com/images2/GradExams/E1E336DB-6F15-4579-89B8-FE039B799486.png' height='14' width='17'/>, then<br><img src='https://www.fatskills.com/images2/GradExams/8B13178A-1194-4C15-9128-2366F6A0F9AB.png' height='20' width='37'/> is convergent in the sense of<br><img src='https://www.fatskills.com/images2/GradExams/FA34593F-686D-487F-A186-47F5BA4EFED0.png' height='22' width='53'/>.





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