True or False: Is there a measurable function $f: \mathbb{R} \to (0,\infty)$ such that $\int \chi_I f d\lambda = \infty$ for every nonempty open interval $I \subset \mathbb{R}$ where $\lambda$ represents Lebesgue Measure on $\mathbb{R}$?  I am pretty sure there is such a function as I am not able to prove the statement. However, I cannot think of an example.
Could give some examples of nonnegative measurable function $f:\mathbb{R}\to[0,\infty)$, such that its integral over any bounded interval is infinite?
StackExchange drop down hiding chat, blog and log out, concerns I know that : $\mathbf{Q}(\sqrt{2}) = \mathbf{Q}+ \sqrt{2} \mathbf{Q}$ , but then what is $\mathbf{Q}(\sqrt{2},\sqrt{3})$? How do I hide posts matching my ignored tags? Where and how do I go about hiding the posts that match any of the tags on my ignored list? What is the rule to convert the 'mm' notation to the 'optical zoom' notation? I searched a bit and found this one:  optical zoom = maximum focal length / minimum focal length   For example a 18-55mm lens would have a 3x optical zoom, and a 18-200mm lens would have a 11x optical zoom. Is that right? Process substitution and pipe I was wondering how to understand the following:     Piping the stdout of a command into the stdin of another is a powerful   technique. But, what if you need to pipe the stdout of multiple   commands? This is where process substitution comes in.   In other words, can process substitution  do whatever pipe can do?   What can process substitution do, but pipe cannot? How to list available shells for use by command-line? Regression - How do I know if my residuals are normally distributed? How to do multiple lines within braces? What makes a good jump scare? I am working on a game and would like to include a few jump scares. So here is a rather simple question — What makes a good jump scare and when and how should they happen? Two-Weapon Fighting & Bonus Actions During the latest gaming session our level 3 Rogue was Two-Weapon fighting with a Rapier in the main-hand and a scimitar in the off-hand.  At the completion of our gaming session I contested the application of the Two-Weapon fighting rules as it seemed unbalanced.  Once I got home I reviewed the PHB and various RPGStack and Reddit but couldn't find a concrete answer.  My interpretation of the PHB Reference rules below is that although any class/character can technically wield a weapon in their off-hand, only those who have been granted a Bonus Action for which no explicit bonus action have been defined would be allowed to actually attack.  So in the case of a Rogue the Bonus Actions granted under Cunning Action allow for specific actions (none of which are attack).  The alternate interpretation would be the rules under Two-Weapon Fighting, perhaps it should be written      you receive a bonus action to attack with a different light melee weapon that you’re holding in the other hand.   This would, in my opinion, explicitly grant the Bonus Action to any character/class who is Two-Weapon Fighting.  After thorough review does it boil down to application of the rules-as-written and determining a house-rule to apply in our campaign?    References  Page 189 of PHB : Bonus Actions  Various class features, spells, and other abilities let you take an additional action on your turn called a bonus action. The Cunning Action feature, for example, allows a rogue to take a bonus action.      You can take a bonus action only when a special ability, spell, or other feature of the game states that you can do something as a bonus   action. You otherwise don’t have a bonus action to take.   You can take only one bonus action on your turn, so you must choose which bonus action to use when you have more than one available. You choose when to take a bonus action during your turn, unless the bonus action’s timing is specified, and anything that deprives you of your ability to take actions also prevents you from taking a bonus action.  Page 96 of PHB  A Rogue receives cunning action at level 2, You can take a bonus action on each of your turns in combat.      This action can be used only to take the Dash, Disengage, or Hide action.   Page 195 of PHB  Two-Weapon Fighting (Combat Rules)  When you take the Attack action and attack with a light melee weapon that you’re holding in one hand, you can use a bonus action to attack with a different light melee weapon that you’re holding in the other hand. You don’t add your ability modifier to the damage of the bonus attack, unless that modifier is negative. If either weapon has the thrown property, you can throw the weapon, instead of making a melee attack with it.  Page 165 of PHB  Dual Wielder  (Feat)  You master fighting with two weapons, gaining the following benefits:   You gain a +1 bonus to AC while you are wielding a separate melee weapon in each hand. You can use two-weapon fighting even when the one-handed melee weapons you are wielding aren't light. You can draw or stow two one-handed weapons when you would normally be able to draw or stow only one. How can I get bold math symbols? To make Latin-letter variables bold I can use e.g. \mathbf{a}, but while putting Greek letters or symbols such as \nabla inside \mathbf doesn't cause any errors or warnings, it also doesn't do anything else.  What is the best way to make bold math symbols, in particular Greek letters and \nabla? Trying to show that $\ln(x) = \lim_{n\to\infty} n(x^{1/n} -1)$ How do I show that $\ln(x) = \lim_{n\to\infty} n (x^{1/n} - 1)$?  I ran into this identity on . I haven't been able to find any proof online and my efforts to get from $\ln(x) := \int_1^x \frac{\mathrm dt}t$ to that limit have been a failure. How to hide the [@] in a Minecraft command block How do the tens­es and as­pects in English cor­re­spond tem­po­ral­ly to one an­oth­er? Non-na­tive speak­ers of­ten get con­fused about what the var­i­ous tens­es  and as­pects mean in English. With in­put from some of the folk here I've put to­geth­er a di­a­gram that I hope will pro­vide some clar­i­ty on the mat­ter.  I of­fer it as the first an­swer to this ques­tion. Con­sid­er it a liv­ing doc­u­ment. In­put is wel­come, and good sug­ges­tions will be  in­cor­po­rat­ed in­to the di­a­gram.    No­ta bene: What this is not is a dis­cus­sion of whether there are  more than two tens­es in English. , to which this ques­tion is not in­tend­ed to sup­ply ar­gu­ments one way or the oth­er.  Here, the aim is to pro­vide an overview of what con­struc­tions English-speak­ing peo­ple use for con­vey­ing in­for­ma­tion about ac­tions re­fer­ring to past, present, and fu­ture, and to pro­vide it first and fore­most to pre­cise­ly the peo­ple who are like­ly to use "tense" as a catch-all term in their search, rather than to lin­guists who know bet­ter.  Break­ing News There is now an ex­cel­lent ELU blog ar­ti­cle ti­tled  . It is high­ly rec­om­mend­ed read­ing. Render looks "brighter" than in viewport preview Somehow my viewport preview shows darker result than what comes out in render (check out in corner of the pic)  World strength is at zero and ambient occlusion is also disabled.  Floor is using bump and roughness from picture. Wall has adaptive subdivision surface  modifier.  All lit using planes with emission shaders.  I wanted to play around with render layers and maybe I screw some setting there, hope this helps. What test can I use to compare slopes from two or more regression models? How to login to gamecenter at PewDiePie's Tuber Simulator? How do I login to the Gamecenter on PewDiePie's Tuber Simulator, if you have not done it when they asked? Solve $\sum nx^n$ I am trying to find a closed form solution for $\sum_{n\ge0} nx^n\text{, where }\lvert x \rvert&lt;1$.  This solution makes sense to me:  $\sum_{n\ge0} x^n=(1-x)^{-1} \\ \frac{d}{d x} \sum_{n\ge0} x^n = \frac{d}{d x} (1-x)^{-1} \\ \sum_{n\ge0} nx^{n-1} = (1-x)^{-2} \\ x \sum_{n\ge0} n x^{n-1} = x(1-x)^{-2} \\ \sum_{n\ge0} nx^n=\frac x{(1-x)^2}$  However, a  I am reading used the following method:  $$\sum_{n\ge0}nx^n=\sum_{n\ge0}x\frac d{dx}x^n= x\frac d{dx}\sum\limits_{n\ge0}x^n=x\frac d{dx}\frac1{1-x}=\frac x{(1-x)^2}$$  This seems closely related to the solution I described above, but I am having difficulty understanding it.  Can someone explain the method being used here? I know it existed as sort of a folder in Windows Explorer in at least Windows XP, but I just can't seem to find it in Windows 7...  How can I take a picture with my webcam in Windows 7 without using any 3rd party tools? Finding $\int \frac{dx}{a+b \cos x}$ without Weierstrass substitution. I saw somewhere on Math Stack that there was a way of finding integrals in the form $$\int \frac{dx}{a+b \cos x}$$ without using Weierstrass substitution, which is the usual technique.   When $a,b=1$ we can just multiply the numerator and denominator by $1-\cos x$ and that solves the problem nicely.   But I remember that the technique I saw was a nice way of evaluating these even when $a,b\neq 1$.