Newbetuts
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New posts in measure-theory
How to properly define conditional probabilities on metric spaces?
probability
measure-theory
random-variables
measurable-functions
borel-measures
Is the probability density function unique?
measure-theory
probability-theory
The number of members of a sigma algebra generated by a set of finite number of subsets of $A$
measure-theory
Absolute continuity of a measure in the intervals implies absolute continuity of borel measures?
measure-theory
absolute-continuity
monotone-class-theorem
Countably generated $\sigma$-algebra implies separability of $L^p$ spaces
general-topology
measure-theory
lp-spaces
Prove that a field of a set has $2^r$ elements if it has finite cardinality.
combinatorics
measure-theory
cardinals
Proof of countable additive property of Lebesgue Integrable functions
measure-theory
lebesgue-integral
sequence-of-function
Measure and metric
measure-theory
metric-spaces
definition
Significance of $\sigma$-finite measures
general-topology
measure-theory
intuition
$\int_X |f_n - f| \,dm \leq \frac{1}{n^2}$ for all $n \geq 1$ $\implies$ $f_n \rightarrow f$ a.e.
measure-theory
convergence-divergence
lebesgue-integral
If $f(x) \le f(Tx)$ then $f(x)=f(Tx)$ almost everywhere ( $T$ is $\mu$-invariant )
measure-theory
dynamical-systems
ergodic-theory
Proof that the Lebesgue measure is complete
measure-theory
lebesgue-measure
Sequence of simple functions nonnegative that converge to measurable function $f$
real-analysis
measure-theory
How do I evaluate the Lebesgue measure of a ball?
real-analysis
measure-theory
Conditional expectation given an event is equivalent to conditional expectation given the sigma algebra generated by the event
probability-theory
measure-theory
conditional-expectation
If X and Y are random variables with the same distribution, prove that f(X) and f(Y) are random variables that have the same distribution.
measure-theory
probability-theory
How to prove $E\subset R^n$ Jordan measurable is equivalent to $\bar{E}-E$ is Jordan measured null
real-analysis
measure-theory
Show that $\phi \circ f$ belongs to $L_p$ for each $f \in L_p$
measure-theory
lp-spaces
Volume of $n$ dimensional ellipsoid
real-analysis
linear-algebra
integration
measure-theory
Pull the teeth out of Lebesgue integration
soft-question
measure-theory
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