• Title: Test Functions

  • Series: Distributions

  • YouTube-Title: Distributions 2 | Test Functions

  • Bright video: https://youtu.be/500gENxWiSU

  • Dark video: https://youtu.be/qtcqQxVzBZs

  • Quiz: Test your knowledge

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  • Subtitle on GitHub: dt02_sub_eng.srt missing

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  • Quiz Content

    Q1: What does the notation $C_c^\infty( \mathbb{R}^n)$ mean?

    A1: The set of all differentiable functions.

    A2: The set of all functions that are arbitrarily often differentiable and have compact support.

    A3: The set of all functions that are arbitrarily often differentiable and that have value 0 at the origin.

    A4: The set of all continuous functions with compact support.

    Q2: How many elements does the set $C_c^\infty( \mathbb{R}^n)$ have?

    A1: Only one, the zero function.

    A2: Infinitely many.

    Q3: What is the correct definition for the support of a function $f$?

    A1: $$ \mathrm{supp}(f) = { x \in \mathbb{R}^n \mid f(x) \neq 0 } $$

    A2: $$ \mathrm{supp}(f) = \overline{{ x \in \mathbb{R}^n \mid f(x) \neq 0 }} $$

    A3: $$ \mathrm{supp}(f) = \overline{{ x \in \mathbb{R}^n \mid f(x) = 0 }} $$

    A4: $$ \mathrm{supp}(f) = { x \in \mathbb{R}^n \mid f(x) = 0 } $$

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