# Tagged Questions

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### problem of integration by substitution [closed]

Hello everyone I have a question which is not of research level but I would like someone gives the related reference for this issue. Let $\mu:=\mu(dx)$ be a probability measure on $\mathbb{R}$ such ...
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### Integrating over the Intersection of Convex Regions

Is there a way to integrate over the intersection of a finite collection of convex regions, using only the definition of the regions (i.e. without actually calculating the intersections)? The ...
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### Defining definite integral using indefinite integral.

Sometimes definite integral is defined using antiderivatives: $$\int_{a}^b{f(t)dt}=F(b)-F(a)$$ where $F$ is any continuous function such that: (\forall t\in[a,b]\setminus C)(F'(t) \space exists ...
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### Real analytic functions

I am quite confused with some ideas regarding the Real analytic functions. Just to introduce my questions: A function $f$ is real analytic on an open set $D$ of the real line if for any $x_0\in D$ ...
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### Gauge integral of the derivative of a function except on a set of measure 0.

For the entire question, the interval I am integrating over is $[0,1]$. Background: In order to exhibit an isometry from $L^2[0,1]$ into $l^2$, I need to either assume absolute continuity over some ...