List questions from simple-functions

Published on 06 Sep 2021 - 4:36

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Proof clarification measure given by integral

Published on 22 Sep 2021 - 14:07

335

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L2 convergence for a simple function approximation

Published on 01 Oct 2021 - 9:40

343

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A Question on Theorem 4.3 of Stein-Shakarchi [Approximating measurable functions with step functions]

Published on 26 Feb 2026 - 4:18

332

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Showing the absolute value of a simple function is a simple function:

Published on 01 Nov 2021 - 17:48

145

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Existence of Locally (Lebesgue-)Integrable Function

Published on 17 Nov 2021 - 13:40

269

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Fubini's theorem for conditional measures

Published on 19 Nov 2021 - 23:50

84

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Does there exist a constant $C>0$ such that for all simple functions $f$, $\int_1^\infty|f|\leq C(\int_1^\infty|f|^p)^{1/p}$?

Published on 06 Jan 2022 - 1:37

89

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Lebesgue integration from definition

Published on 15 Feb 2022 - 21:56

197

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Why proof of linearity of integration for simple functions requires non-negative coefficients?

Published on 03 Mar 2022 - 9:23

157

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Folland Theorem 6.14: Why is $ \lim |\int f_n g | \leq M_q(g)$?

Published on 06 Mar 2022 - 17:18

116

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Question related to approximation of measurable functions by simple functions

Published on 27 Feb 2026 - 5:57

213

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Show that $\phi_n(x) \leq \phi_{n+1}(x)$ (Folland Theorem 2.10)

Published on 12 Apr 2022 - 12:53

36

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A question on the integral of nonnegative functions using the integral of simple functions

Published on 24 Apr 2022 - 1:35

24

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Question involving integration of nonnegative measurable functions using simple functions

Published on 25 Apr 2022 - 23:56

List Question

Representation of Simple Function

Proof clarification measure given by integral

L2 convergence for a simple function approximation

A Question on Theorem 4.3 of Stein-Shakarchi [Approximating measurable functions with step functions]

Showing the absolute value of a simple function is a simple function:

Existence of Locally (Lebesgue-)Integrable Function

Fubini's theorem for conditional measures

Does there exist a constant $C>0$ such that for all simple functions $f$, $\int_1^\infty|f|\leq C(\int_1^\infty|f|^p)^{1/p}$?

Lebesgue integration from definition

Why proof of linearity of integration for simple functions requires non-negative coefficients?

Folland Theorem 6.14: Why is $ \lim |\int f_n g | \leq M_q(g)$?

Question related to approximation of measurable functions by simple functions

Show that $\phi_n(x) \leq \phi_{n+1}(x)$ (Folland Theorem 2.10)

A question on the integral of nonnegative functions using the integral of simple functions

Question involving integration of nonnegative measurable functions using simple functions

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